A dam seepage edge real-time inversion method based on physical information neural network

Abstract

This invention discloses a real-time inversion method for seepage edge analysis in dams based on a physical information neural network, belonging to the field of water conservancy engineering safety monitoring technology. The method includes: collecting and preprocessing multi-source monitoring data on seepage pressure, temperature, and deformation; constructing a seepage-temperature-deformation coupling mechanism model; constructing a physical information neural network, embedding the partial differential equations of seepage mechanics as physical constraints into the loss function, and using hard constraint boundary conditions; lightweighting the model and deploying it on edge computing nodes to achieve real-time seepage field inversion; and performing streamline tracing and comprehensive anomaly index calculation based on the inversion results to identify abnormal seepage paths and provide graded early warnings. This invention achieves technical effects such as an inversion accuracy R²=0.97, low equation residuals, short single inversion time (seconds), and anomaly identification accuracy of 94%, and can be widely applied to seepage safety monitoring of reservoirs, dams, dikes, and tailings ponds.

Description

Technical Field

[0001] This invention relates to the field of water conservancy engineering safety monitoring technology, specifically to a real-time inversion method for dam seepage edge based on physical information neural network, applicable to seepage field inversion and abnormal seepage path identification of reservoir dams, dikes, and tailings ponds. Background Technology

[0002] my country has built approximately 98,000 dams and reservoirs of various types, with a total length of over 300,000 kilometers of dikes and nearly 10,000 tailings ponds, ranking first in the world in terms of quantity. These water conservancy infrastructures play an irreplaceable role in flood control, water supply, power generation, and irrigation. However, the seepage safety problem they face during long-term operation is becoming increasingly prominent. Statistical data shows that seepage failure is one of the main causes of dam failure, accounting for more than 40% of earth-rock dam failures. Seepage hazards are characterized by their high degree of concealment and suddenness. Traditional manual inspections and point monitoring are insufficient to detect abnormal seepage paths in a timely manner. Once the seepage deteriorates, it can lead to seepage damage such as piping and soil erosion, ultimately resulting in dam failure.

[0003] With the rapid development of sensing technology, the Internet of Things, and artificial intelligence, dam safety monitoring has entered a new stage of "big data + intelligence." The widespread application of new monitoring equipment such as BeiDou high-precision positioning, fiber optic sensing, and MEMS piezometers enables engineering managers to obtain real-time information on dam deformation, seepage pressure, temperature, and other multi-physical fields. However, a significant gap remains between the explosive growth of monitoring data and the ability to intelligently assess seepage conditions. How to quickly and accurately invert the internal seepage field of the dam from multi-source monitoring data, identify potential seepage paths, and achieve a leap from "data perception" to "state cognition" has become a key scientific problem urgently needing breakthroughs in the field of water conservancy engineering.

[0004] Current seepage inversion methods are mainly divided into three categories: indirect methods based on optimization theory, data-driven deep learning methods, and physical information neural network methods. However, existing technologies have the following technical shortcomings:

[0005] (1) Lack of physical consistency in pure data-driven models

[0006] While deep learning methods such as Convolutional Neural Networks (CNNs), Long Short-Term Memory Networks (LSTMs), and Graph Neural Networks (GNNs) demonstrate excellent fitting capabilities, they are entirely dependent on the quality and quantity of training data. When monitoring data is limited, noisy, or exceeds the distribution range of the training samples, model predictions may violate Darcy's law and the principle of mass conservation, resulting in physically unacceptable seepage field outcomes. For example, a purely data-driven model might predict seepage flow from low head to high head, violating the second law of thermodynamics, or introduce singularities in the head field that do not meet the smoothness requirements of the Laplace equation.

[0007] (2) Insufficient integration and utilization of multi-source monitoring data

[0008] Existing research often focuses on single data types (such as seepage pressure data), failing to adequately explore the coupling relationships between temperature, deformation, and seepage fields. In reality, changes in the seepage field can cause temperature anomalies (seepage heat transport effect). The higher the seepage velocity, the more significant the convective heat transport effect, leading to localized temperature anomalies. Simultaneously, seepage generates seepage forces, altering the effective stress of the dam body and consequently causing deformation responses. Single-field data is insufficient to comprehensively capture the seepage state, and existing fusion methods are mostly simple feature splicing or decision weighting, failing to fully utilize the physical mechanisms of multi-field coupling.

[0009] (3) Insufficient real-time inversion capability

[0010] Traditional finite element inversion methods require repeated calls to the forward solver, with each iteration needing to solve a large system of sparse linear equations, resulting in high computational costs; a single inversion typically takes tens of minutes to several hours. While Physical Information Neural Networks (PINNs) achieve integrated forward and inversion solutions, existing PINN models typically have around 10 parameters. 5 ~10 6 The scale is enormous; a single forward inference takes hundreds of milliseconds to several seconds on a CPU, and model training requires a large number of data points and multiple iterations, making it difficult to achieve real-time operation on resource-constrained edge nodes, thus restricting the need for rapid on-site response.

[0011] (4) Weak automatic identification technology for abnormal seepage paths

[0012] Most studies stop at seepage field inversion, lacking effective methods for automatically extracting abnormal seepage paths from the inversion results. Traditional methods often rely on manual interpretation of contour maps or profiles, which are highly subjective and inefficient. A few automated methods rely solely on a single indicator (such as the absolute value of the permeability coefficient) for threshold judgment, resulting in a high false alarm rate and failing to provide connectivity information and evolution trends of seepage channels. Consequently, the inversion results are difficult to directly translate into actionable information for identifying potential engineering hazards.

[0013] (5) Boundary condition handling is not precise enough

[0014] Existing PINN methods often employ soft constraints to handle boundary conditions, incorporating boundary errors as a penalty term into the loss function. However, soft constraints can only approximately satisfy the boundary conditions, and the penalty coefficients require careful adjustment: too small a coefficient leads to large boundary errors, while too large a coefficient dominates the loss function, affecting data fitting and equation residual optimization. For dams with complex geometries, accurate satisfaction of boundary conditions is particularly important, directly impacting the reliability of the inversion results.

[0015] (6) Lack of model update mechanism

[0016] Dam operating conditions are time-varying; seasonal changes in reservoir water levels, aging of dam materials, and accumulation of seismic damage can all alter seepage characteristics. Existing methods mostly employ static models, lacking dynamic update mechanisms to adapt to changing operating conditions. Retraining the model would require uploading large amounts of raw data to a cloud center, consuming significant communication bandwidth and raising concerns about data security and privacy. Summary of the Invention

[0017] The purpose of this invention is to overcome the shortcomings of the prior art and provide a real-time inversion method for dam seepage edges based on physical information neural networks. Through multi-field perception fusion, physical constraint dual-drive, real-time edge inversion and abnormal path identification, it can achieve high-precision inversion of the seepage field and intelligent early warning of seepage hazards.

[0018] To achieve the above objectives, the present invention provides the following technical solution:

[0019] A real-time inversion method for dam seepage edge based on physical information neural networks, characterized by the following steps:

[0020] Step 1: Data Acquisition and Preprocessing from Multiple Monitoring Sites

[0021] Data on seepage pressure, temperature field, and deformation of the dam body were collected. The collected raw monitoring data were cleaned to remove noise and outliers. The cleaned multi-source monitoring data were spatiotemporally aligned to obtain a multi-field monitoring dataset in a unified spatiotemporal coordinate system. The spatiotemporally aligned multi-field monitoring data were normalized to construct a multi-field perception fusion feature vector.

[0022] Furthermore, the spatiotemporal alignment of multi-field monitoring data in step 1 includes: resampling other monitoring data based on the lowest sampling frequency to achieve time alignment; and mapping point-based monitoring data to a unified spatial discrete grid using radial basis function interpolation or kriging interpolation to achieve spatial alignment.

[0023] Furthermore, the data cleaning in step 1 includes: removing high-frequency noise using moving average, wavelet denoising, or Kalman filtering; and using... Outliers are identified and removed using criteria, box plots, and physical constraints. For short-term missing data, linear interpolation or spline interpolation is used to fill in the missing data. For long-term missing data, an ARIMA model is built based on historical data from the same period to predict and fill in the missing data.

[0024] Furthermore, in step 1, the normalization process employs minimum-maximum normalization or Z-score standardization to map each physical quantity to a unified dimension range.

[0025] Step 2: Construct a coupled mechanism model of seepage-temperature-deformation

[0026] The coupling mechanism between the seepage field and the temperature field is analyzed, and the convection-diffusion equation for seepage heat transport is established:

[0027]

[0028] in, For temperature, For Darcy velocity, and These represent the density and specific heat capacity of the porous medium, respectively. and For the density and specific heat capacity of the fluid, The thermal conductivity coefficient, This is a heat source term.

[0029] The coupling mechanism between the seepage field and the deformation field is analyzed, and a coupling relationship based on the effective stress principle is established:

[0030]

[0031] in, For the total stress, For effective stress, Pore ​​water pressure, For Biot coefficient, Let Kronecker function be used.

[0032] Establish constitutive relations for multi-field coupling, considering the feedback of temperature and deformation fields on the permeability coefficient:

[0033]

[0034] in, For reference permeability coefficient, Let temperature be the function. This is the volumetric strain influence function.

[0035] Step 3: Construct a physical information neural network inversion model

[0036] A fully connected neural network consisting of an input layer, a hidden layer, and an output layer is constructed; the input layer receives spatiotemporal coordinates and boundary condition indicator variables; the output layer outputs the head field and the permeability coefficient field.

[0037] Furthermore, the fully connected neural network employs a residual connection structure:

[0038]

[0039] in, For the activation function, use tanh or Swish. and For network weights and biases, This represents the number of network layers.

[0040] The partial differential equation of seepage mechanics is used as the loss function embedded in the neural network as a physical constraint. The partial differential equation of seepage mechanics is as follows:

[0041]

[0042] in, Water content by volume For pressure head, For the total water head, For location head, It is a function of the permeability coefficient. For source and sink terms, saturated seepage simplifies to:

[0043]

[0044] in, This represents the water storage coefficient.

[0045] A hard constraint boundary condition processing method is adopted, which forces the neural network output to accurately satisfy the boundary conditions through network output transformation. The hard constraint transformation function is:

[0046]

[0047] in, For point The distance function to the Dirichlet boundary, This is the original output from the network. This is the final output after transformation. The head value is known for the boundary.

[0048] For mixed boundary conditions, a more general transformation form is constructed:

[0049]

[0050] in and The algorithm is constructed based on boundary conditions, and the specific steps are as follows:

[0051] Algorithm 1: Hard Constraint Boundary Transformation

[0052] 1. Calculate the Dirichlet boundary distance function.

[0053] 2. Calculate the Neumann boundary distance function.

[0054] 3. Construct auxiliary functions ,make sure

[0055] 4. Construct auxiliary functions Satisfy: In superior,

[0056] 5. Order

[0057] Construct a multi-field fusion loss function, including the fitting error term of the seepage observation data, the residual term of the seepage equation, the temperature field coupling constraint term, and the deformation field coupling constraint term:

[0058]

[0059] in:

[0060]

[0061]

[0062]

[0063]

[0064] in, The inverted seepage velocity, For the inverted pore water pressure, , , These are the balancing weighting coefficients.

[0065] An adaptive weight adjustment strategy is adopted to dynamically adjust the weights based on the gradient magnitude of each loss term:

[0066]

[0067] in For the first The gradient of the loss term, This is the reference gradient.

[0068] The neural network parameters are trained by minimizing the multi-field fusion loss function, using the Adam optimizer, with an initial learning rate of [missing information]. Training rounds: 5000-10000; batch size: 128-256.

[0069] Step 4: Lightweight Model Processing

[0070] The trained physical information neural network is subjected to lightweight processing, which includes model pruning, knowledge distillation, and computation graph optimization.

[0071] Furthermore, the model pruning includes: evaluating the importance of each neuron based on the L2 norm of the neuron output weights, with the importance index being:

[0072]

[0073] in This is the weight vector connecting the neuron to the next layer. Neurons with importance below a preset threshold are removed. An iterative pruning-fine-tuning strategy is used, pruning 10% of neurons each time, then fine-tuning to restore accuracy, repeating until the target compression ratio is achieved.

[0074] Furthermore, the knowledge distillation includes: training a lightweight student network using the original physical information neural network as the teacher network. The distillation loss function is:

[0075]

[0076] in The fitting error of the student network on the observed data, This represents the mean squared error between the student's network output and the teacher's network output. This is the balance coefficient.

[0077] Furthermore, the computation graph optimization includes operator fusion (merging consecutive matrix multiplications, bias additions, and activation functions into a single operator), constant folding (pre-computing the static part), memory reuse, and quantization processing. The quantization processing converts 32-bit floating-point parameters to 16-bit floating-point or 8-bit integers, and quantization error compensation uses:

[0078]

[0079] in The number of bits used for quantization.

[0080] Step 5: Edge Node Deployment and Real-time Inference

[0081] The lightweight physical information neural network model is deployed on the edge computing nodes in the dam area; the edge computing nodes receive the multi-field monitoring data after preprocessing in step 1 in real time, perform forward inference of the model, and output the inverted head field and permeability coefficient field.

[0082] Furthermore, the edge computing nodes adopt an edge-cloud collaborative architecture: the cloud center is responsible for large-scale historical data training, model version management, and complex working condition simulation; the edge nodes are responsible for real-time response, on-site inversion, and anomaly warning; and the terminal perception layer is responsible for data collection and transmission.

[0083] Furthermore, the real-time inference adopts an asynchronous pipeline architecture, which pipelines and parallelizes data acquisition, preprocessing, model inference, and result reporting, and implements it using a producer-consumer model with multiple threads.

[0084] Furthermore, the method also includes a model update step: the edge computing node caches recent monitoring data, and when the inversion error exceeds a preset threshold or an update instruction is received from the cloud center, the cached data is used to incrementally fine-tune the lightweight model and update the model parameters. The incremental fine-tuning uses a small learning rate. Before freezing Layer parameters, only updated after layer.

[0085] Step 6: Identification of Abnormal Seepage Paths

[0086] Based on the water head field obtained in step 5 and permeability field Calculate the hydraulic gradient field:

[0087]

[0088] Calculate the seepage velocity field:

[0089]

[0090] The seepage path is generated using a streamline tracing method, and the streamlines satisfy the differential equation:

[0091]

[0092] in, Let be the arc length along the streamline. The fourth-order Runge-Kutta method is used for numerical solution:

[0093]

[0094]

[0095]

[0096]

[0097]

[0098] Starting points are evenly distributed across the upstream dam surface, and the flow is traced along the direction of velocity until the downstream boundary or seepage outlet is reached.

[0099] Extract seepage characteristic parameters, including the permeability coefficient anomaly index, hydraulic gradient anomaly index, and seepage velocity anomaly index:

[0100]

[0101]

[0102]

[0103] in , The mean and standard deviation of the permeability coefficient. , The mean and standard deviation of the hydraulic gradient are given. , The mean and standard deviation of the seepage velocity are given.

[0104] Constructing a comprehensive anomaly index :

[0105]

[0106] in Mapping the exponents of the Sigmoid function to interval, , , For the corresponding weight coefficients, satisfying .

[0107] Furthermore, the weighting coefficients are determined based on engineering experience or the analytic hierarchy process (AHP), with typical values ​​being [value missing]. , , .

[0108] Classified early warning of seepage paths based on comprehensive anomaly index:

[0109] when When the time is blue, it indicates a potential anomaly and requires enhanced monitoring.

[0110] when At this time, it is a yellow warning level, indicating that there is a significant abnormality and expert consultation is required;

[0111] when At this time, it is an orange alert level, indicating that there is a serious anomaly and on-site verification is required;

[0112] when At this time, it is a red alert level, indicating that there is an urgent hidden danger that needs to be dealt with immediately.

[0113] Furthermore, a time-series evolution analysis was performed on the identified abnormal seepage paths to calculate the rate of change of abnormal intensity:

[0114]

[0115] The rate of expansion of anomaly area and the migration trajectory of anomaly center should be given priority for rapidly developing anomalies.

[0116] Step 7: 3D Visualization and Decision Support

[0117] Develop a 3D visualization interface based on WebGL technology, and implement the following functions:

[0118] Permeability coefficient field cloud map display (profile / 3D volume rendering)

[0119] Superposition of head contour lines and streamlines

[0120] Abnormal areas are highlighted

[0121] Slide the timeline to view historical inversion results

[0122] Early warning information is pushed to relevant personnel through monitoring platform pop-ups, SMS / WeChat message pushes, and automatically generated early warning reports.

[0123] Beneficial effects

[0124] Compared with the prior art, the present invention has the following beneficial effects:

[0125] (1) Innovative effects of multi-field perception fusion

[0126] This invention constructs a multi-field sensing fusion mechanism encompassing pressure, temperature, and deformation, performing spatiotemporal alignment and feature fusion of multi-source monitoring data. Furthermore, it introduces coupling constraints between the temperature and deformation fields into the loss function, achieving deep integration of multi-source data with physical mechanisms. Compared to traditional feature-level or decision-level fusion, this invention's physically guided coupling fusion method ensures that temperature and deformation field information truly participates in seepage inversion constraints, improving the inversion accuracy R² from 0.88 to 0.97 and the anomaly identification accuracy from 75% to 94%.

[0127] (2) The innovative effect of physical constraint embedding

[0128] This invention embeds the partial differential equations of seepage mechanics as physical constraints into a neural network and employs a hard constraint boundary condition processing method. By transforming the network output, the boundary conditions are forced to be met, thus resolving the physical inconsistency problem in purely data-driven models. Compared to soft constraint methods, hard constraints reduce boundary condition errors by two orders of magnitude, and the residuals of the seepage equation decrease from... Reduce to The accuracy of penetration coefficient inversion is improved by more than 15%, and the extrapolation capability in sparse regions of training data is significantly enhanced.

[0129] (3) Innovative effects of edge real-time inversion

[0130] This invention lightweights the physical information neural network through model pruning, knowledge distillation, and quantization optimization. The number of model parameters is compressed from 528K to 56K, achieving a compression rate of 89.4%; inference time is reduced from 156ms to 23ms, a speedup of 6.8 times; and memory usage is reduced from 124MB to 21MB, a reduction of 83.1%. The lightweight model was successfully deployed on the edge computing nodes of the dam area, enabling real-time inversion of the seepage field. The end-to-end time for a single inversion is controlled within 3 seconds, meeting the real-time response requirements of the project.

[0131] (4) Innovative effects of abnormal path identification

[0132] This invention, based on the inverted permeability coefficient field and hydraulic head field, constructs a streamline tracking algorithm and a multi-index fusion discrimination method. By comprehensively considering permeability coefficient anomalies, hydraulic gradient anomalies, and seepage velocity anomalies, it achieves automated identification and graded early warning of abnormal seepage channels. Physical model experiments verify that the preset artificial channel locations were successfully identified, with a comprehensive anomaly index reaching 0.92 (orange warning level). In practical engineering applications, it successfully identified an abnormal seepage area on the right bank dam section, and on-site exploration confirmed its accuracy. The implemented grouting treatment effectively reduced the seepage flow.

[0133] (5) The innovative effect of dynamic model updating

[0134] This invention designs an edge incremental learning mechanism. When changes in operating conditions cause the inversion error to exceed the limit, edge nodes use cached data to fine-tune and update the model without uploading the original data to the cloud center. Incremental learning restores the error from over 5% to within 3%, while protecting data privacy, reducing communication bandwidth consumption, and achieving dynamic adaptation of the model.

[0135] (6) Wide range of engineering applicability

[0136] The method of this invention is not only applicable to reservoir dams, but can also be extended to water conservancy and geotechnical engineering fields involving seepage safety, such as dike projects, tailings ponds, and underground water-sealed caverns, and has important engineering application value and social and economic benefits. Attached Figure Description

[0137] Figure 1 This is an overall flowchart of the method of the present invention.

[0138] Figure 2 This is a flowchart of the multi-field monitoring data preprocessing process in this invention.

[0139] Figure 3 This is a schematic diagram of the seepage-temperature-deformation coupling mechanism in this invention.

[0140] Figure 4 This is a schematic diagram of the physical information neural network in this invention.

[0141] Figure 5 The diagram below illustrates the hard constraint boundary condition processing in this invention: (a) original network output; (b) distance function; (c) output after hard constraint transformation.

[0142] Figure 6 This is a flowchart of the adaptive weight adjustment strategy in this invention.

[0143] Figure 7 This is a flowchart of the model lightweighting process in this invention.

[0144] Figure 8 This is a schematic diagram of the edge-cloud collaborative architecture in this invention.

[0145] Figure 9 This is a flowchart of abnormal seepage path identification in this invention.

[0146] Figure 10 This is a schematic diagram of the graded early warning strategy in this invention.

[0147] Figure 11 This is a layout diagram of the physical model of the earth-rock dam in Embodiment 1 of the present invention.

[0148] Figure 12 The following is a comparison of the inversion results in Embodiment 1 of the present invention: (a) the actual permeability coefficient field; (b) the inversion result of the method of the present invention; (c) the inversion result of the pure data-driven method.

[0149] Figure 13 This is a diagram showing the results of identifying abnormal seepage paths in Embodiment 1 of the present invention.

[0150] Figure 14 This is a diagram showing the layout of the monitoring section of an actual engineering dam in Embodiment 2 of the present invention.

[0151] Figure 15 This is a cloud map of the inverted permeability coefficient field in Embodiment 2 of the present invention.

[0152] Figure 16 This is a diagram showing the results of streamline tracing and abnormal region identification in Embodiment 2 of the present invention.

[0153] Figure 17 This is a diagram showing the results of on-site exploration and verification in Embodiment 2 of the present invention.

[0154] Figure 18 This is a schematic diagram of the three-dimensional visualization interface in this invention. Detailed Implementation

[0155] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments.

[0156] Example 1: Physical Model Experiment Verification

[0157] This embodiment verifies the effectiveness of the method of the present invention on a physical model of an earth-rock dam, specifically according to... Figure 1 The overall process is as shown.

[0158] Step 1: Data Acquisition and Preprocessing from Multiple Monitoring Sites

[0159] like Figure 11 As shown, a physical model of an earth-rock dam is constructed with the following dimensions: dam height 1.5m, dam crest width 0.6m, dam base width 4.5m, and upstream / downstream slope ratio 1:2. The dam body is filled with gravel and sand. An artificial seepage channel (a permeable pipe, 5cm in diameter, located at 0.8m dam height, with a horizontal length of 1.2m) is pre-installed within the dam body. The monitoring system layout includes:

[0160] Pressure monitoring: Vibrating wire piezometers are used, with 15 gauges in 3 rows of 5 points each, with an accuracy of ±0.1%FS and a sampling frequency of 10 minutes / time;

[0161] Temperature monitoring: Distributed fiber optic DTS is used, with a spatial resolution of 0.5m, a temperature resolution of 0.1℃, and a sampling frequency of 1 minute / time;

[0162] Deformation monitoring: 8 surface displacement markers (measured using a total station), 3 internal settlement meters (using a stratified settlement meter), sampling frequency 2 hours / time.

[0163] Test conditions: upstream water level 1.2m, stable seepage for 24 hours; artificial channel opened at the 12th hour to simulate abnormal seepage.

[0164] like Figure 2 The data preprocessing workflow shown here processes the raw monitoring data:

[0165] (1) Data cleaning: High-frequency noise was removed by moving average method with a window size of 5; outliers were identified by 3σ criterion and 3 obvious outliers were removed; linear interpolation was used to supplement short-term missing data (<3 consecutive sampling points).

[0166] (2) Spatiotemporal alignment: Temporal alignment is based on the sampling frequency of osmotic pressure data (10 minutes / time), temperature data is resampled (rounded to the measurement value at 10-minute intervals), and linear interpolation is used for deformation data to obtain the corresponding values ​​at those times. Spatial alignment uses Kriging interpolation to map the point monitoring data to a 0.1m × 0.1m spatial grid, and a spherical model is used for the variogram model.

[0167]

[0168] in For nugget constant, For sill values, For variable range.

[0169] (3) Normalization: Min-max normalization is used to map each physical quantity to Interval:

[0170]

[0171] Step 2: Construct a coupled mechanism model of seepage-temperature-deformation

[0172] like Figure 3 As shown, the multi-field coupling mechanism is analyzed. The coupling between the seepage field and the temperature field is described by the convection-diffusion equation:

[0173]

[0174] Soil parameters: , , , , .

[0175] The coupling between the seepage field and the deformation field is based on the effective stress principle:

[0176]

[0177] Take the Biot coefficient (Soil), pore water pressure .

[0178] Step 3: Construct a physical information neural network inversion model

[0179] like Figure 4 As shown, a physical information neural network is constructed:

[0180] Input layer: Receives spatial coordinates and time There are a total of 3 neurons.

[0181] Hidden layers: An 8-layer fully connected network with 128 neurons per layer, using tanh activation function and residual connections.

[0182] Output layer: Output head field And logarithmic permeability field There are a total of 2 neurons.

[0183] Residual connection structure:

[0184]

[0185]

[0186]

[0187]

[0188] The partial differential equations of seepage mechanics adopt the saturated seepage control equations:

[0189]

[0190] Water storage coefficient .

[0191] like Figure 5 As shown, hard constraint boundary conditions are used. The distance function from each point to the Dirichlet boundary is calculated. The upstream boundary ( , ) Downstream boundary ( , ) Other boundaries are impermeable boundaries (Neumann boundaries) Construct the transformation function:

[0192]

[0193] The multi-field fusion loss function is constructed as follows:

[0194]

[0195] in:

[0196] Mean square error of 15 piezometer observation points

[0197] The mean square error of the equation residuals on 1000 randomly sampled collocation points within the computational domain.

[0198] Temperature field coupling constraint, constructed based on 50 temperature measurement points.

[0199] Deformation field coupling constraints, constructed based on 11 deformation measurement points.

[0200] like Figure 6 As shown, an adaptive weight adjustment strategy is adopted, updating the weights every 500 rounds to keep the gradient magnitudes of each loss term relatively equal.

[0201] The network parameters are trained using the Adam optimizer, with an initial learning rate of... The training run consisted of 5000 epochs with a batch size of 128. Every 500 epochs during training, the model was saved, and the model with the smallest error on the validation set was selected as the final model.

[0202] Step 4: Lightweight Model Processing

[0203] like Figure 7 As shown, the original PINN model after training is subjected to lightweight processing:

[0204] (1) Model pruning: The importance of each neuron is evaluated based on the L2 norm of the output weights. The 30% of neurons with the lowest importance are removed layer by layer. After pruning, the accuracy is restored by fine-tuning for 100 rounds. This process is repeated 3 times. The original model has 528K parameters (8×128×128 structure), and the pruned model has 265K parameters (6×100×100 structure).

[0205] (2) Knowledge distillation: Using the original PINN as the teacher network, a student network (4 layers × 50 neurons) is constructed. The distillation loss function is minimized over 10,000 collocations:

[0206]

[0207] After 3000 training rounds, the final number of student network parameters reached 56K.

[0208] (3) Quantization: Convert the model parameters from FP32 to INT8 using symmetric quantization.

[0209]

[0210] (4) Computation graph optimization: TensorRT is used to perform operator fusion and memory optimization on the model, and matrix multiplication, bias addition and ReLU activation are fused into a single operator.

[0211] Step 5: Edge Node Deployment and Real-time Inference

[0212] like Figure 8 As shown, the lightweight model is deployed on a Jetson AGX Orin edge computing node (4-core CPU + 256-core GPU, 8GB memory). The edge node receives and monitors the data stream in real time, using an asynchronous pipeline architecture.

[0213] Thread 1: Data Acquisition and Caching (Collected every 10 minutes)

[0214] Thread 2: Data Preprocessing (Sliding Window, 24 Time Steps)

[0215] Thread 3: Model Inference (Batch Size 1)

[0216] Thread 4: Result Post-processing and Reporting

[0217] Test results show that the average time for a single inference is 23ms, and the end-to-end inversion time (including data preprocessing and visualization output) is 2.7 seconds.

[0218] Step 6: Identification of Abnormal Seepage Paths

[0219] like Figure 9 As shown, abnormal path identification is performed based on the inversion results. The inverted head field is... and permeability field ,calculate:

[0220] Hydraulic gradient field:

[0221]

[0222] Seepage velocity field:

[0223]

[0224] Streamline tracing is performed using the fourth-order Runge-Kutta method, with a step size of [missing information]. 50 starting points were evenly set up from the upstream dam face. Track along the direction of flow velocity until reaching the downstream boundary or .

[0225] Extract feature parameters:

[0226] , ,

[0227] Calculated , , , , , .

[0228] Construct a comprehensive anomaly index:

[0229]

[0230] in This is the Sigmoid function.

[0231] like Figure 10 The tiered early warning strategy shown pre-sets the flow path of the manual passage area. This corresponds to an orange alert level.

[0232] like Figure 12 The inversion results shown are compared, and the permeability field inverted by the method of this invention ( Figure 12 b) and the real field ( Figure 12 a) Highly consistent and accurately identifies the location of manual channels; while the pure data-driven LSTM method ( Figure 12 c) The channel morphology cannot be accurately reconstructed, and multiple false anomalies are generated.

[0233] like Figure 13The abnormal path identification results show that the streamlines converge in the artificial channel area, and the flow velocity increases, successfully locating the abnormal seepage location. The anomaly identification accuracy is 94%, and the recall rate is 92%.

[0234] Step 7: 3D Visualization and Decision Support

[0235] like Figure 18 As shown, a 3D visualization interface was developed based on Three.js, enabling functions such as permeability coefficient field cloud maps, streamline overlay, and highlighting of abnormal areas. Warning information is pushed to administrators via platform pop-ups and SMS messages.

[0236] Example 2: Practical Engineering Application

[0237] This embodiment verifies the practicality of the method of the present invention on a large earth-rock dam project.

[0238] Project Overview: The dam is 86m high, 450m long at the crest, and has a reservoir capacity of 230 million m³. It has been in operation for 25 years. In recent years, localized wet areas have appeared at the downstream toe of the slope, suspected to be abnormal seepage. Figure 14 As shown, the monitoring system includes:

[0239] Piezometers: 42 units, distributed across 3 monitoring sections (0+150, 0+235, 0+320), with 3 rows of 5 points per section, plus 6 points at the dam foundation.

[0240] Temperature monitoring: DTS fiber optic cable is embedded in the core wall, with a total length of 350m and a spatial resolution of 1m.

[0241] Deformation monitoring: 6 Beidou monitoring stations (surface displacement), 4 inclinometer boreholes (internal horizontal displacement), and 12 settlement gauges.

[0242] Nearly 3 years of monitoring data were collected (January 2023 - December 2025), totaling approximately 150,000 data points on seepage pressure, continuous recording of temperature data (every 10 minutes), and deformation data twice a week.

[0243] Data preparation and model training:

[0244] Data preprocessing was the same as in Example 1, with a focus on analyzing section 0+235. Kriging interpolation was used to map the point data to a two-dimensional profile grid (87×50 nodes, grid size 1m×1m). Data from January 2023 to June 2025 was selected as the training set (80%), and data from July 2025 to December 2025 was selected as the test set (20%).

[0245] The original PINN model was trained in a cloud center (configured with 4×GPU Tesla V100). Considering the layered filling characteristics of the actual dam body, the permeability coefficient is expressed as:

[0246]

[0247] in Let the eigenfunction be the feature function of the KL expansion, and take... Training parameters: Network depth 10 layers, width 200, learning rate... Round 8000, loss weight , , .

[0248] After training, the distillation loss is calculated using a knowledge distillation compression model (teacher network 10×200, student network 6×80). The model was trained for 2000 epochs. After lightweighting, the number of model parameters was compressed from 1.2M to 96K, a compression rate of 92%.

[0249] Edge Deployment: An edge server (NVIDIA Jetson AGX Orin, 2 units with primary and backup redundancy) is deployed at the dam area management center, and connected to various monitoring devices via industrial Ethernet. The edge nodes perform an inversion calculation every 30 minutes (configurable), and the results are stored in a local database and reported to the cloud center.

[0250] Inversion results and verification:

[0251] like Figure 15 As shown, the real-time inversion results of the edge nodes indicate that the permeability coefficient is abnormal in the area between 580m and 600m elevation at section 0+235 on the right bank dam section. 1.2 higher than the mean (corresponding to) (Value 3.3 times higher), comprehensive abnormality index (Yellow alert level).

[0252] like Figure 16 As shown, streamline tracing reveals a suspected seepage channel in this area, with dense streamlines pointing towards the downstream slope toe wet zone. The flow through the abnormal area accounts for 23% of the total flow, with a hydraulic gradient of 0.45 (compared to 0.15-0.25 in the normal area).

[0253] On-site exploration and verification ( Figure 17 Core sampling was conducted in the abnormal area (3 boreholes, 25-30m deep). It was found that the backfill density was low (dry density 1.52g / cm³, design requirement 1.65g / cm³), with localized fine particle loss. Permeability tests showed... (Design value) This confirmed the accuracy of the inversion results. The subsequent grouting treatment (injection of 58 tons of cement grout) effectively reduced the seepage flow, eliminated the wet zone, and reduced the seepage flow at the downstream toe of the slope from 12.5 L / min to 3.2 L / min.

[0254] Performance comparisons are shown in Table 1:

[0255] Table 1. Performance Comparison of Several Methods

[0256] method Inversion accuracy (R²) Anomaly detection accuracy Single calculation time Equation residuals Finite element inversion (genetic algorithm) 0.91 82% 45 min <![CDATA[1.2×10 -4 ]]> LSTM 0.88 75% <1 s Unconstrained PINN (Soft Constraint) 0.94 88% 2.3 s <![CDATA[8.7×10 -3 ]]> This method 0.97 94% 2.9 s <![CDATA[2.3×10 -4 ]]>

[0257] Model update:

[0258] In August 2025, the reservoir water level plummeted from 85m to 72m (due to flood discharge scheduling). Edge nodes detected an increase in the inversion error from 3.2% to 6.8% (exceeding the 5% threshold), automatically triggering incremental learning. The model was fine-tuned using cached data from the last 7 days (350 samples), with a learning rate of... The parameters of the first four layers were frozen, and the last two layers were updated. After 100 rounds of fine-tuning, the error was restored to 2.9%. The entire process took 8.7 minutes and did not require uploading the original data to the cloud center.

[0259] Example 3: Comparative Experiment

[0260] To verify the contributions of each innovative aspect of this invention, an ablation experiment was designed:

[0261] Experiment A: No multi-field fusion (using only osmotic pressure data)

[0262] Experiment B: No non-physical constraints (purely data-driven LSTM)

[0263] Experiment C: Soft Constraint Boundaries (Replacing Hard Constraints)

[0264] Experiment D: No lightweighting (original model cloud inference)

[0265] Experiment E: Complete Method of the Invention

[0266] The comparison results on the physical model data of Example 1 are shown in Table 2:

[0267] Table 2. Experimental Comparison Results

[0268] experiment Inversion error (RMSE) Physical residuals Boundary error Reasoning time Anomaly detection accuracy A 0.087 <![CDATA[5.6×10 -3 ]]> <![CDATA[3.2×10 -3 ]]> 28 ms 86% B 0.156 Unconstrained <![CDATA[1.8×10 -2 ]]> 15 ms 75% C 0.063 <![CDATA[8.7×10 -3 ]]> <![CDATA[7.5×10 -3 ]]> 26 ms 88% D 0.042 <![CDATA[2.5×10 -4 ]]> <![CDATA[<10 -6 ]]> 156 ms 95% E 0.038 <![CDATA[2.3×10 -4 ]]> <![CDATA[<10 -6 ]]> 23 ms 94%

[0269] The results show that:

[0270] Multi-field fusion reduced the inversion error by 12.6% (comparison between A and E).

[0271] Physical constraints reduced the error by 75.6% (compare B and E).

[0272] Hard constraints reduce boundary errors by three orders of magnitude (compare C and E).

[0273] Lightweight design speeds up inference time by 6.8 times (compared to D and E).

[0274] Industrial Application Prospects

[0275] The method of this invention can be widely applied in the following scenarios:

[0276] (1) Reservoir dams: Applicable to seepage safety monitoring of various dam types (earth-rock dams, concrete dams, masonry dams), especially for screening hidden dangers of old dams that have been in operation for many years.

[0277] (2) Embankment Engineering: Used for early warning of dangers such as piping and seepage in embankments. Combined with drone inspection, it can realize rapid inspection of long-distance embankments.

[0278] (3) Tailings dam: Tailings dam failure accidents occur frequently. This method can be used for tailings dam wetting line inversion and seepage stability analysis.

[0279] (4) Underground water-sealed cavern: suitable for monitoring the seepage field of strategic petroleum reserves and underground gas storage facilities.

[0280] (5) Slope engineering: It can be used for seepage stability analysis of highway and railway slopes and to identify potential landslide hazards.

[0281] Summary of technical effects

[0282] In summary, this invention achieves the following technical effects through innovative designs including multi-field perception fusion, dual-drive of physical constraints, real-time edge inversion, and abnormal path identification:

[0283] (1) High-precision inversion: The inversion accuracy R² = 0.97 and the relative error < 5%, which is significantly better than existing methods;

[0284] (2) Strong physical consistency: the residual of the seepage equation is <10⁻³, and the boundary conditions are precisely satisfied;

[0285] (3) Real-time response: The end-to-end time for a single inversion is less than 3 seconds, which meets the requirements for rapid on-site response;

[0286] (4) Intelligent early warning: The anomaly identification accuracy rate is 94%, providing tiered early warning and visual display;

[0287] (5) Dynamic adaptation: Supports incremental model updates to adapt to changes in working conditions.

[0288] Industrial Applicability Notes

[0289] The method of this invention has been successfully applied in a large earth-rock dam project. The system has been running stably for 6 months, completing a total of 8760 inversion calculations, and successfully providing early warning for 3 areas of abnormal seepage. The accuracy has been verified on-site, effectively guiding the project maintenance. The system deployment cost is approximately 150,000 yuan (including edge node hardware and software development), which is far lower than the cost of traditional manual inspection and geophysical exploration (approximately 300,000-500,000 yuan per year), demonstrating good economic benefits and promotional value.

[0290] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Those skilled in the art can make various improvements and modifications without departing from the spirit and principles of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A real-time inversion method for dam seepage edge based on physical information neural networks, characterized in that, Includes the following steps: Step 1: Collect seepage pressure monitoring data, temperature field monitoring data, and deformation monitoring data of the dam body; perform data cleaning on the collected raw monitoring data to remove noise and outliers; The cleaned multi-source monitoring data is spatiotemporally aligned to obtain a multi-field monitoring dataset in a unified spatiotemporal coordinate system; the spatiotemporally aligned multi-field monitoring data is normalized to construct a multi-field perception fusion feature vector. Step 2: Construct a physical information neural network inversion model, which includes an input layer, a hidden layer, and an output layer; the input layer receives spatiotemporal coordinates and boundary condition indicator variables; the output layer outputs the head field. and permeability field ; the partial differential equations of seepage mechanics The loss function is embedded in the neural network as a physical constraint; a hard constraint boundary condition processing method is adopted, through the transformation function. Compulsive nerves The network output precisely satisfies the boundary conditions, where For point The distance function to the Dirichlet boundary, This is the original output from the network. Given a known head value at the boundary; construct a multi-field fusion loss function, and train the neural network parameters by minimizing the multi-field fusion loss function; Step 3: Lightweight the trained physical information neural network and deploy the lightweight physical information neural network model on the edge computing nodes in the dam area; the edge computing nodes receive the multi-field monitoring data preprocessed in Step 1 in real time, perform forward inference of the model, and output the inverted head field and permeability coefficient field. Step 4: Based on the head field obtained in step 3 and permeability field The seepage path is generated using a streamline tracing method, and the streamlines satisfy the differential equation. ,in Let be the arc length along the streamline. The seepage velocity vector is used to extract seepage characteristic parameters and construct a comprehensive anomaly index. ,in This is the permeability anomaly index. This is the hydraulic gradient anomaly index. This is the anomaly index of seepage velocity. For the Sigmoid function, , , The weighting coefficient is used to classify and warn of seepage paths based on the comprehensive anomaly index, and to identify abnormal seepage channels.

2. The method according to claim 1, characterized in that, The multi-field fusion loss function in step 2 is: in This is the fitting error term for the seepage pressure observation data. This is the residual term of the seepage equation. For temperature field coupling constraints, For deformation field coupling constraint terms, , , These are the balancing weighting coefficients.

3. The method according to claim 1, characterized in that, The lightweighting process in step 3 includes model pruning, knowledge distillation, and computation graph optimization. The model pruning evaluates the importance of neurons based on the L2 norm of the neuron output weights and removes neurons whose importance is below a preset threshold. The knowledge distillation uses the original physical information neural network as the teacher network to train a lightweight student network. The computation graph optimization includes operator fusion, constant folding, memory reuse, and quantization.

4. The method according to claim 1, characterized in that, The tiered early warning strategy in step 4 is as follows: when At the time, the attention level is blue. The current alert level is yellow. At the time, the alert level was orange. The alert level was red.

5. The method according to claim 1, characterized in that, It also includes a model update step: edge computing nodes cache recent monitoring data, and when the inversion error exceeds a preset threshold or an update instruction is received from the cloud center, the cached data is used to incrementally fine-tune the lightweight model and update the model parameters.

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