A method and system for real-time prediction of embankment breach edge collapse

Abstract

The present application relates to the technical field of water conservancy emergency rescue, and discloses a dike breach edge collapse real-time prediction method and system, wherein the method comprises the following steps: S1, acquiring on-site multi-source monitoring data of the breach, performing spatial interpolation on the discrete monitoring data, and deducing static force balance based on a soil constitutive model to reconstruct a three-dimensional state field at the current time; S2, inputting the current state field and hydrological boundary conditions into a spectrum self-adaptive physical constraint Fourier neural operator model, deducing each time through error correction autoregression iteration, and outputting a three-dimensional state field prediction sequence of a future set time period. The present application realizes second-level high-precision advanced prediction of the breach edge collapse by decomposing and competitively self-adaptively weighting three types of physical constraint residuals of momentum, mass and collapse critical criteria in the Fourier frequency domain, combining error correction autoregression with Lyapunov stability constraint and time-coupled damage surface evolution tracking, and the prediction is stable and does not diverge, and can be quantitatively connected with rescue decision-making such as head wrapping and rescue, anchoring, etc.

Description

Technical Field

[0001] This invention relates to the field of water conservancy emergency rescue technology. Background Technology

[0002] After a levee breach occurs, the water flow velocity at the breach can reach over 8.5 m / s. The continuous scouring of the edge soil by the high-speed water flow causes it to erode and peel away, easily inducing sudden secondary collapses and seriously threatening the safety of personnel working on the levee and rescue equipment. The physical essence of the collapse at the breach edge is a spatiotemporal dynamic evolution process of "water scouring—soil weakening—local instability—gradual expansion". Existing levee slope stability analysis relies on the limit equilibrium method or finite element static calculation, which is essentially based on static cross-sectional analysis and cannot capture the entire dynamic evolution process mentioned above. Although high-fidelity three-dimensional fluid-structure interaction numerical simulation can accurately reproduce the collapse process, a single simulation takes several hours to several days, which is sharply contradictory to the millisecond-level decision-making requirements at the rescue site.

[0003] In recent years, artificial intelligence has been introduced into the rapid assessment of soil and rock slope stability, but three systemic shortcomings remain. First, traditional data-driven models such as BP neural networks and WAGA-BP only establish a black-box mapping of "input-safety factor," lacking constraints from fundamental soil mechanics equations. Under unseen conditions such as extreme flow velocities and sudden piping, they are prone to producing distorted predictions that violate physical laws. Second, safety factor calculations generally employ the assumption of a fixed sliding surface or overall cross-sectional averaging, failing to locate scattered, small high-risk areas and neglecting the continuous evolution of the failure surface over time, simplifying gradual failure into discrete static snapshots. Third, early warning systems primarily rely on threshold discrimination, lacking quantitative integration with emergency response parameters. The models are not lightweighted for field-level equipment, making them difficult to operate independently in flood emergency response environments without network connectivity or large-scale computing power.

[0004] Even in the more cutting-edge field of "physically constrained deep learning," key gaps remain in current technology. Fourier Neural Operators (FNOs), as novel operator learning architectures for solving partial differential equations, possess a natural frequency domain computational structure. However, existing methods of embedding physical information in FNOs, such as "Fourier Feature-Based PINN" (applying learnable Fourier feature maps to the input and then superimposing residual losses with fixed weights) and "Physically Embedded Fourier Neural Operators" (using external solver residuals as a single regularization term), do not utilize the residual information of the FNO spectral computation itself across various frequency bands to drive adaptive weighting of physical constraints. Existing gradient-based adaptive weighting strategies (such as gradient maximization and exponential normalization based on the rate of change of loss) only utilize the relative magnitude of scalar losses and cannot achieve decoupling of physical constraints across spatial frequency scales. However, levee collapse prediction precisely requires this frequency band differentiation: stress concentration areas are high-frequency features, large-scale erosion is a low-frequency feature, and shear bands are mid-frequency features. In addition, existing slope stability monitoring and early warning systems mainly rely on multi-source sensing, time-frequency characteristics, and graded early warning. Their safety factor uses the static failure surface searched independently at each time point, without linking the evolution of the failure surface with the prediction confidence level and emergency construction parameters. Summary of the Invention

[0005] The purpose of this invention is to provide a real-time prediction method and system for the collapse of the edge of a dike breach. This method can compress the three-dimensional fluid-structure interaction simulation, which originally took several hours to several days, into a single inference at the millisecond level. By combining mechanisms such as frequency band-level physical constraint adaptive decoupling, error correction autoregression and Lyapunov stability constraint, and time-coupled failure surface evolution tracking, it achieves high-precision advance prediction of the collapse of the edge of the breach at the second level. The prediction is stable and does not diverge, and it can be quantitatively integrated with emergency decision-making such as headwork and anchoring.

[0006] To address the aforementioned technical problems, this invention provides a method for real-time prediction of levee breach edge collapse, comprising the following steps: S1. Obtain multi-source monitoring data at the breach site, perform spatial interpolation on the discrete monitoring data, and conduct static equilibrium deduction based on the soil constitutive model to reconstruct the three-dimensional state field at the current moment. S2. Input the current three-dimensional state field and the hydrological boundary conditions within a set future time period into the trained spectrum adaptive physical constraint Fourier neural operator model. Through error correction autoregression iteration, the model is deduced time by time and outputs a three-dimensional state field prediction sequence covering the set future time period. S3. Based on the predicted three-dimensional stress field, a time-coupled failure surface evolution tracking method is adopted to apply time continuity constraints to the potential failure surface at each time step, to determine the potential failure surface of each spatial point at each prediction time, and to calculate the local safety factor of each spatial point in real time according to the Mohr-Coulomb criterion. S4. When the local safety factor is lower than the preset threshold, a graded warning is issued and the corresponding quantitative emergency rescue construction parameters are output.

[0007] The training loss used during training of the Fourier neural operator model Data-driven loss terms The training loss is composed of a spectrum-adaptive physical constraint loss term, which decomposes the residuals of three types of physical constraints—momentum conservation, mass conservation, and collapse criticality criterion—in the Fourier frequency domain by frequency band, and adaptively allocates the weights of each constraint within each frequency band using a competitive mechanism. The expression is: In the formula, For data-driven loss terms; The total number of physical constraint categories, including at least three categories: momentum conservation, mass conservation, and collapse criticality criterion. This represents the total number of frequency bands. This refers to the physical constraint category number; Frequency band number; For a specific moment; For the first Frequency characterization of each frequency band; for Time of the first Physically constrained residuals in frequency band Fourier coefficients at the location; for Time of the first Class constraints in the first Adaptive weighting for each frequency band; This represents the L2 norm.

[0008] The data-driven loss term Determine using the following formula: In the formula, This represents the total number of spatial grid points in a single training batch. For grid point numbers; For the first The coordinates of each spatial grid point; and The first The predicted state field vector and the true state field vector at each spatial grid point; and They are respectively Time of the first Predicted local safety factor and true local safety factor at each spatial grid point; This is the weighting coefficient for the local safety factor loss. The residuals of the three types of physical constraints—momentum conservation, mass conservation, and collapse critical criterion—are determined by the following formulas: In the formula, , and They are respectively Time of the first Momentum conservation residuals, mass conservation residuals, and collapse critical criterion residuals at each spatial grid point; For spatial points The density of the soil at that location; for Time and Space Point The velocity vector of the soil skeleton; for Time and Space Point Stress tensor at the point; Represents the divergence operator; It is the vector of gravitational acceleration; It is a linear rectified function; for Time of the first The predicted local safety factor for each spatial grid point is calculated based on the predicted stress field.

[0009] The first Class constraints in the first Adaptive weighting of each frequency band The competitive normalization mechanism based on frequency band spectral energy is used, and the result is determined according to the following formula: In the formula, For the first Baseline weights for class constraints; This is the competition intensity coefficient; For the first Class constraints in the first Spectral energy of each frequency band; To sum the physical constraint category numbers in the index; The frequency band spectrum energy Update the exponential moving average as follows: In the formula, The moving average decay rate; For time step; for Time of the first Physically constrained residuals in frequency band Fourier coefficients at the location.

[0010] In step S2, during the error correction autoregressive iteration, the first... The three-dimensional state field at time t is determined by the following formula: In the formula, for The three-dimensional state field at any given time; for The three-dimensional state field at any given time; for The state field increment output by the Fourier neural operator model at time t; for The time error correction term is determined by the following formula: In the formula, To correct the step size; This represents the total number of physical constraint categories. For the first Weights of physical constraints; for Time of the first Physically constrained residuals; Represents the state field vector in three dimensions Find the gradient.

[0011] The correction step size Satisfying the Lyapunov stability constraint, the Lyapunov stability constraint is: Let the energy function be... When the correction step size When the exponential decay condition is satisfied The upper limit of the correction step size Determine using the following formula: In the formula, The expected error decay rate; is the Lipschitz constant of the Fourier neural operator model; For the first Weights of physical constraints; For the first The gradient of the physical constraint residual with respect to the three-dimensional state field; Represents the L2 norm; This indicates taking the maximum value; the correction step size Take as .

[0012] The Fourier neural operator model embeds a physically guided spatial attention module between each Fourier layer. This module, based on channel-dimensional global average pooling and channel-dimensional global max pooling, introduces the predicted stress tensor divergence norm as the physical attention signal, generating a spatial attention weight map for each spatial point. Determine using the following formula: In the formula, The feature map output by the Fourier layer in the Fourier neural operator model; and These are channel-dimensional global average pooling and channel-dimensional global max pooling, respectively. For spatial points Predicted stress tensor at the location; To predict the divergence of the stress tensor; Represents the norm; This indicates a channel splicing operation; These are the kernel weights; This is a convolution operation; This is the Sigmoid activation function.

[0013] The local safety factor in step S3 Calculate using the following formula: In the formula, for Time and Space Point Shear strength of the soil at the location for Time and Space Point The movable shear stress at the potential failure surface is determined by the following formulas: In the formula, For spatial points The effective cohesion of the soil; For spatial points The effective internal friction angle of the soil at the location; for Time and Space Point Predicted stress tensor at the location; for Time and Space Point Predicted pore water pressure at the location; The unit normal vector of the potential failure surface; The potential failure surface is determined by time-coupled failure surface evolution tracking, and its unit normal vector is... Optimize as follows: In the formula, This refers to the effective normal stress acting on the potential failure surface; This is the time smoothing coefficient; The historical damage memory coefficient; For historical damage memory items; The time derivative of the unit normal vector of the potential failure surface is discretized by the following formula: In the formula, and They are respectively Time and The potential destructive surface normal vector at any given moment; For time step; The historical damage memory item Determine using the following formula: In the formula, To store the length of the memory window; For historical moment sequence numbers; For the time scale of memory; for The unit normal vector of the potential damage surface is determined at any given time; for Soil damage variables at any given time.

[0014] After reconstructing the three-dimensional state field in step S1, the physical consistency data quality of the three-dimensional state field is verified. The verification uses momentum residuals. Determine using the following formula: In the formula, For spatial points The density of the soil at that location; It is the vector of gravitational acceleration; For spatial points The stress tensor obtained from reconstruction; Represents the divergence operator; Represents the norm; When the global mean of the momentum residual Greater than the preset residual threshold When the area with the largest residual is marked as the area with low data confidence, the sampling frequency of the monitoring data in that area is increased, and the data is supplemented and then re-interpolated. In step S4, the confidence level of the prediction result is calculated. Determine using the following formula: In the formula, This represents the total number of physical constraint categories. for Time of the first Physically constrained full-band total spectral energy; For the first The baseline spectral energy of physical constraints during the training convergence period; The tiered early warning is triggered by a joint criterion of local safety factor range and confidence level. and A yellow alert is issued and a list of head-wrapping reinforcement materials and anchorage pre-positioning coordinates are output. An orange alert is issued and the pre-slope reduction depth of the dike head, the volume of earth and stone for emergency construction of the dike head, and the coordinates of the equipment anchoring points are output. A red alert is issued and instructions are sent to evacuate personnel and equipment from the designated area and to activate emergency anchoring; among other things, This is a preset threshold.

[0015] The present invention also provides a real-time prediction system for the collapse at the edge of a dike breach, used to implement the real-time prediction method for the collapse at the edge of a dike breach as described above, comprising: Multi-source data acquisition module, used to acquire multi-source monitoring data; The field state reconstruction module is used to perform spatial interpolation on discrete monitoring data and static equilibrium deduction based on the soil constitutive model to reconstruct the three-dimensional state field at the current moment. The field state reconstruction module is equipped with a data quality verification submodule, which is used to perform physical consistency verification on the reconstructed three-dimensional state field based on momentum residuals. The edge reasoning module is internally deployed with a trained spectrum adaptive physical constraint Fourier neural operator model, which is used to receive the three-dimensional state field and hydrological boundary conditions, and output a three-dimensional state field prediction sequence covering a future set time period through error correction autoregression iterative output. The real-time assessment module for collapse critical values ​​is used to determine potential failure surfaces based on the predicted three-dimensional stress field by employing time-coupled failure surface evolution tracking, and to calculate the local safety factor for each spatial point according to the Mohr-Coulomb criterion. The early warning and decision output module is used to generate graded early warnings and corresponding quantitative emergency rescue construction parameters when the local safety factor is lower than the preset threshold, and send them to the on-site control platform. A visualization terminal is used to display the collapse evolution process, local safety factor cloud map, and the curve of change in the effective passage width of the embankment top in real time.

[0016] Compared to existing technologies, this invention deeply embeds the physical knowledge of high-fidelity three-dimensional fluid-structure interaction numerical simulation into the frequency domain structure of neural operators, compressing the high-fidelity simulation that originally took several hours to several days into a single inference within 100ms. Combined with 10s time step autoregression, a complete 40-minute prediction sequence can be completed within 1 to 2 seconds, meeting the second-level decision-making requirements for disaster relief. After knowledge distillation and FP16 quantization, the model can be independently deployed on portable edge devices in the field, and can still autonomously complete all prediction calculations in extreme environments where floods cause base station interruptions and there is no fiber optic network, achieving an order-of-magnitude leap in prediction speed.

[0017] Furthermore, by using spectral adaptive physical constraint loss, the residuals of three types of physical constraints—momentum, mass, and collapse critical criteria—are decomposed into frequency bands in the Fourier frequency domain and competitively weighted. This allows the model to automatically focus on the most severe physical constraint violation at each spatial frequency scale. Compared to fixed weights or gradient scalar weighting schemes, the relative error of the displacement field is reduced by approximately 15% to 20%, and the prediction error of the safety factor is reduced by approximately 10% to 15%. Moreover, it still outputs reasonable predictions that do not violate physical laws even under unseen conditions such as extreme flow velocities and sudden piping. Physically guided spatial attention focuses on the force balance failure zone using stress divergence as a signal, thereby improving the prediction accuracy of local collapse areas. The error correction autoregression is constrained by the Lyapunov exponential decay condition, mathematically ensuring that no error accumulation or divergence occurs in the 240 steps of autoregression iteration, thus solving the traditional long-term "drift" problem.

[0018] In addition, by tracking the evolution of the time-coupled failure surface, the discrete static failure surface is upgraded into a path-dependent continuous evolution trajectory, accurately reproducing the gradual failure process and continuously depicting the spatiotemporal evolution of gradual failure. The three-level early warning uses the joint criterion of "local safety factor × confidence level" to simultaneously output directly verifiable parameters such as the location of the emergency reinforcement of the embankment, the volume of earth and stone for construction, the depth of the pre-slope reduction of the embankment, and the coordinates of the equipment anchoring points. The confidence level index provides a quantifiable and reliable basis for the early warning classification. The rolling prediction mechanism realizes all-weather dynamic tracking of the risk of breach collapse, realizing an integrated closed loop of "risk prediction - intelligent decision-making - mechanized operation" without the need for manual secondary calculation.

[0019] The above description is merely an overview of the technical solution of the present invention. In order to better understand the technical means of the present invention and to implement it in accordance with the contents of the specification, and in order to make the above and other objects, features and advantages of the present invention more apparent and understandable, specific embodiments of the present invention are described below. Attached Figure Description

[0020] One or more embodiments are illustrated by way of example with reference numerals in the accompanying drawings. These illustrations do not constitute a limitation on the embodiments. Elements with the same reference numerals in the drawings are denoted as similar elements. Unless otherwise stated, the figures in the drawings are not to be limited by scale.

[0021] Figure 1 This is a flowchart illustrating at least one embodiment of the present invention; Figure 2 This is a schematic diagram of the module connection relationship in at least one embodiment of the present invention; Figure 3 This is a schematic diagram of the layout of multi-source monitoring data acquisition points at a breach site in one embodiment of the present invention; Figure 4 This is a schematic diagram of the spectrum-adaptive physical constraint Fourier neural operator model structure in one embodiment of the present invention; Figure 5 This is a schematic diagram of the spectrum adaptive physical constraint loss calculation process in one embodiment of the present invention. Detailed Implementation

[0022] To make the objectives, technical solutions, and advantages of this invention clearer, the embodiments of this invention will be described in detail below with reference to the accompanying drawings. However, those skilled in the art will understand that many technical details are presented in the embodiments of this invention to facilitate a better understanding of this application. However, the technical solutions claimed in this application can be implemented even without these technical details and various variations and modifications based on the following embodiments. The division of the following embodiments is for ease of description and should not constitute any limitation on the specific implementation of this invention. The embodiments can be combined with and referenced by each other without contradiction.

[0023] Example 1 like Figure 1 The method for real-time prediction of levee breach edge collapse, as shown, includes the following steps: S1. Acquire multi-source monitoring data at the breach site and reconstruct the three-dimensional state field at the current moment. Multi-source sensors are deployed on both sides of the breach and in the edge areas of the dike that may collapse. The multi-source monitoring data includes the displacement vector of the dike top surface, the horizontal displacement sequence of the soil along the depth direction, the spatial distribution of pore water pressure, and the water level process line and flow velocity process line for a future preset time period transmitted wirelessly from the upstream hydrological station. Specifically, global navigation satellite system displacement gauges are arranged at intervals along the dike axis and perpendicular to the dike axis on the dike top surface. Inclinometer holes are drilled along the depth direction inside the dike body and inclinometers are installed in the holes. Pore water pressure gauges are drilled and installed in potential piping areas and near the dike toe. Simultaneously, rolling hydrological forecasts from the upstream hydrological station are received via a wireless communication module. Kriging space interpolation was performed on the aforementioned discrete monitoring data, mapping it to a three-dimensional grid computational domain. Combined with the Duncan-Zhang soil constitutive model, static equilibrium iterative deduction was performed to reconstruct the three-dimensional state field at the current moment. This three-dimensional state field includes the displacement vector field, stress tensor field, pore water pressure field, and soil damage variable field, i.e. ,in In three-dimensional space coordinates, This refers to the current moment.

[0024] Generally, the soil damage variable D(x,t) is a scalar field with a value range of [0,1]: D=0 indicates that the soil is in an initial undamaged state, and D=1 indicates that the soil is completely destroyed and its bearing capacity is basically lost.

[0025] Damage variables are calculated based on the cumulative evolution of equivalent plastic strain, and are used in the numerical simulation training samples according to the following formula: In the formula for Time and Space Point Equivalent plastic strain at the point, The equivalent plastic strain threshold at soil failure is 0.03 for silty clay and 0.05 for sand and gravel.

[0026] In the SA-PC-FNO model prediction, the damage variable is one of the output components of the three-dimensional state field. It is directly predicted by the model through autoregressive iteration and reflects the coupling effect of water flow scouring, stress redistribution and material degradation.

[0027] S2. Input the current three-dimensional state field and the hydrological boundary conditions for the next set time period into the trained spectral adaptive physical constraint Fourier neural operator (SA-PC-FNO) model. This model uses a Fourier neural operator as its backbone network, inputting the initial state field and the hydrological boundary condition feature vector encoded by time convolution, and outputting the state field increment at a single time step. During inference, iterates step-by-step through error-corrected autoregressive iteration: input the current state field and the boundary condition encoding vector for the corresponding time period into the model to obtain the state field for the next time period. Then, use the prediction result of the next time period as the new initial field, combining it with the boundary conditions for the next time period, and repeat the iteration until a three-dimensional state field prediction sequence covering the entire future set time period is generated.

[0028] Generally, temporal convolutional coding is implemented using a two-layer one-dimensional convolutional network: the first layer has a kernel size of 5 and 16 output channels, and the second layer has a kernel size of 3 and 32 output channels; the input is the water level process line and flow velocity process line within a future set time period (sampling interval Δt=10s), and after two layers of convolution, a boundary condition feature vector with a dimension of 32 is obtained through global average pooling.

[0029] The feature vector is fused with the initial state field at the input layer through channel-wise concatenation, and together they serve as the input to the FNO model.

[0030] S3. Based on the predicted three-dimensional stress field, time-coupled failure surface evolution tracking is used to determine the potential failure surface of each spatial point at each predicted time. The local safety factor of each spatial point is calculated in real time according to the Mohr-Coulomb criterion. The predicted three-dimensional stress field is decomposed point-by-point using eigenvalue decomposition to obtain the maximum and minimum principal stresses. By considering the continuous evolution of the failure surface normal vector in the time dimension, the potential failure surface orientation of each spatial point at each time is determined. Subsequently, the local safety factor of each spatial point is calculated according to the Mohr-Coulomb criterion, forming a local safety factor field covering all future predicted times.

[0031] S4. When the local safety factor is lower than the preset threshold, a graded early warning is issued and corresponding quantitative emergency construction parameters are output. The system traverses the predicted time and spatial area to identify dangerous areas where the local safety factor is lower than the preset threshold and outputs graded early warning signals. At the same time, based on the spatial range and evolution trend of the dangerous area, it quantifies and generates emergency construction parameters such as the location of the embankment reinforcement, the volume of earth and stone to be reinforced, the pre-slope depth of the embankment, and the coordinates of the equipment anchoring points, which are then directly executed by on-site personnel and emergency equipment.

[0032] One specific calculation method for the above-mentioned quantitative emergency rescue construction parameters is as follows: (1) Location of the head wrapping: The geometric center of the largest spatially connected area where the local safety factor is continuously lower than the preset threshold is taken as the head wrapping center. The length of the head wrapping along the embankment axis is taken as the projected length of the dangerous area along the embankment axis plus a safety margin of 5m. The width of the water-facing side is taken as 3m. (2) Volume of earth and stone for emergency construction: estimated by multiplying the geometric volume of the end cap by a loose-laying coefficient of 1.3, i.e. Where L is the length of the embankment head, W is the width of the water-facing side, and H is the sum of the pre-slope depth and the superelevation of the embankment crest; (3) Pre-slope depth at the embankment head: Determined according to the minimum safety factor Fs_min in the hazardous area using the following formula: ,in For the slope depth coefficient, take... = 2.0 m (that is, for every 0.1 decrease in the safety factor, the pre-slope depth increases by 0.2 m), and adjustments are made based on the actual depth of the scour pit at the embankment head; (4) Coordinates of the anchoring point: Take the anchoring point as 5m outward from both ends of the rear edge of the dangerous area along the embankment axis, and ensure that the anchoring point is located in a stable area with a safety factor greater than 1.2.

[0033] By embedding high-fidelity three-dimensional fluid-structure interaction physics knowledge into a neural network model, the model can output the displacement field, stress field, and failure zone evolution sequence for a future period within seconds. Compared to traditional static analysis, it can capture the continuous dynamic evolution of water erosion, soil weakening, local instability, and even overall collapse. Compared to high-fidelity numerical simulation, it significantly shortens the time required for a single prediction, meeting the real-time decision-making needs at breach rescue sites. It quantifies the risk of collapse at the breach edge into a grid-by-grid, time-by-time local safety factor cloud map, simultaneously locating scattered and small high-risk areas. This provides a quantitative basis for subsequent graded early warning and precise rescue, significantly improving the real-time nature and scientific rigor of rescue safety assurance.

[0034] Example 2 Based on Example 1, the training loss consists of a data-driven loss term and a spectrum-adaptive physical constraint loss term. Training Loss ,in For data-driven loss terms; The total number of physical constraint categories, including at least three categories: momentum conservation, mass conservation, and collapse criticality criterion (in this embodiment) ); Total number of frequency bands (in this embodiment) ); for Time of the first Physically constrained residuals in frequency band The Fourier coefficients at the point are directly extracted in situ from the FNO spectral layer, without the need for additional Fourier transform computational overhead; for Time of the first Class constraints in the first Adaptive weights for each frequency band. The data-driven loss term synchronously fits the true values ​​of the state field and the local safety factor, expressed as follows: ,in The local safety factor loss weighting coefficient (taken in this embodiment) ).

[0035] The residuals for the three types of physical constraints are defined as follows: Momentum conservation residuals mass conservation residual Collapse Critical Criterion Residual Among them, the momentum conservation residual characterizes the unbalanced quantity of the soil skeleton motion equation, the mass conservation residual characterizes the mass conservation condition of the continuous medium, and the collapse critical criterion residual imposes a linear penalty when the predicted local safety factor is less than 1, forcing the model to strictly follow the soil mechanics collapse critical physical condition.

[0036] The adaptive weights for each frequency band are determined using a competitive normalization mechanism based on the frequency band spectral energy, expressed as follows: , of which Class constraints in the first The spectral energy of each frequency band is updated by exponential moving average using the following formula: In this embodiment, the competition intensity coefficient Moving average decay rate The benchmark weights corresponding to momentum, mass, and collapse criticality criteria are respectively taken as follows: , , .

[0037] The state reconstruction phase introduces data quality verification based on physical consistency. Momentum residual verification is performed on the initially reconstructed stress field, and the momentum residual is... , For spatial points The density of the soil at that location It is the gravitational acceleration vector. The reconstructed stress tensor. When the global mean... Greater than the preset residual threshold (In this embodiment) When the residual is at its maximum, the region with the highest residual is marked as the region with low data confidence. This triggers the doubling of the sampling frequency of the GNSS displacement gauge and pore pressure gauge in that region. After supplementing the data, the data is re-interpolated and reconstructed.

[0038] The confidence level of the prediction results is calculated during the early warning output stage. ,in for Time of the first Physically constrained full-band total spectral energy For the first The baseline spectral energy of the physical constraints during the training convergence period. A three-level early warning is triggered using a joint criterion of local safety factor interval and confidence level: when... A yellow alert is triggered when the confidence level is greater than 0.7, and a list of reinforcement materials for the head wrap and the pre-positioning coordinates of the anchorage are output; when When an orange alert is triggered, the pre-slope depth of the dike head, the volume of earth and stone for emergency construction of the dike head, and the coordinates of the equipment anchoring points are output; when A red alert is triggered, and instructions are issued to evacuate personnel and equipment from the designated area and to activate emergency anchoring. A preset threshold is included. The value range is 1.05 to 1.20.

[0039] This decouples the three types of physical constraints in the Fourier frequency domain and utilizes the competition mechanism of frequency band spectral energy to dynamically allocate physical constraint weights in a two-dimensional space of "constraint category × frequency band". This allows the model to automatically focus on the most severely violated physical constraints at each spatial frequency scale: strengthening momentum conservation in the high-frequency band to capture stress concentration areas, strengthening mass conservation in the low-frequency band to eliminate volume anomalies, and strengthening collapse criteria in the mid-frequency band to calibrate shear bands. Compared to fixed weights or schemes that only adjust weights according to gradient scalars, this mechanism significantly improves the physical rationality of predictions under extreme conditions and effectively reduces the relative error of the displacement field and the prediction error of the safety factor. Physical consistency data quality verification can promptly detect and eliminate the contamination of subsequent predictions by abnormal monitoring data, while the confidence index provides a quantifiable reliability basis for early warning grading. Together, these two aspects ensure the accuracy and reliability of the entire prediction process.

[0040] Example 3 Based on Example 1, in the error correction autoregression, the first... The three-dimensional state field at time t is That is, in addition to the state field increment predicted by FNO, an error correction term is superimposed. This allows the reasoning stage to proactively correct itself in a direction that satisfies physical constraints, among which... To correct the step size, For the first Weights of physical constraints, For the first Physically constrained residuals. The correction step size is subject to Lyapunov stability constraints: assuming the energy function... When the correction step size When the exponential decay condition is satisfied The upper limit of the correction step size , The desired error decay rate (taken in this embodiment) ), The model Lipschitz constant is used, and the actual correction step size is taken as... To leave a safety margin.

[0041] The model embeds a physically guided spatial attention module between each Fourier layer. In addition to channel-dimensional global average pooling and max pooling, it introduces the predicted stress tensor divergence norm as a physical attention signal, which is then processed by 3D convolution and a Sigmoid function to generate a spatial attention weight map. ,in This is the feature map output by the Fourier layer. The stress divergence norm directly measures the region of force imbalance, enabling the attention mechanism to adaptively focus on high-risk areas such as scour pits and piping points at the levee toe, achieving a closed loop between "physical quantity" and "attention" without the need for additional sensors.

[0042] In time-coupled failure surface evolution tracking, the local safety factor is calculated according to... Calculate the shear strength. movable shear stress Unlike traditional methods that independently search static damage surfaces at each time step, this embodiment introduces temporal continuity constraints and historical damage memory terms into the optimization of the damage surface normal vector. The unit normal vector... ,in For the effective normal stress, the time derivative term is calculated according to... Discrete, historical damage memory items are In this embodiment, the time smoothing coefficient... Angle from the largest interior point With time step Confirm, memory window length Memory time scale Historical damage memory coefficient .

[0043] In this embodiment, error-corrected autoregression and Lyapunov stability constraints actively apply physical laws during the inference phase and mathematically ensure that long-term autoregressive iterations do not diverge, solving the long-term "drift" problem of traditional autoregression. The learning of physical laws during the training phase and the application of physical laws during the inference phase form a consistent closed loop. Physically guided spatial attention focuses on the force balance failure zone using stress divergence as a signal, significantly improving the prediction accuracy of local collapse areas. Temporally coupled failure surface tracking upgrades discrete static failure surface snapshots into path-dependent continuous evolution trajectories through temporal continuity constraints and historical damage memory terms. The historical damage memory terms enable failure surface searches to actively avoid already damaged locations, accurately depicting the progressive failure process and providing a failure surface basis that better conforms to actual evolution laws for subsequent safety factor calculations and early warnings.

[0044] Example 4 like Figure 2 The system shown is a real-time prediction system for the edge collapse of a dike breach, used to implement Embodiments 1 to 3. It includes a multi-source data acquisition module, a field status reconstruction module, an edge reasoning module, a real-time assessment module for collapse critical values, an early warning and decision output module, and a visualization terminal.

[0045] The multi-source data acquisition module integrates a GNSS receiver unit, an inclinometer acquisition unit, a pore pressure acquisition unit, and a hydrological data wireless transmission unit to acquire multi-source monitoring data at a certain synchronous frequency at the breach site. The site state reconstruction module performs spatial interpolation on the discrete monitoring data and performs static equilibrium deduction based on the soil constitutive model to reconstruct the three-dimensional state field at the current moment. It includes a data quality verification submodule, which performs physical consistency verification on the reconstructed three-dimensional state field based on momentum residuals. When the mean value of the residuals exceeds a threshold, areas with low data confidence are marked and re-acquisition is triggered. The edge inference module internally deploys a spectrum-adaptive physically constrained Fourier neural operator model, trained and lightweight as described above. It receives the three-dimensional state field and hydrological boundary conditions, and outputs a predicted sequence of the three-dimensional state field covering a future set time period through error-corrected autoregressive iteration. The real-time collapse critical value assessment module, based on the predicted three-dimensional stress field, uses time-coupled failure surface evolution tracking to determine potential failure surfaces and calculates the local safety factor for each spatial point in parallel according to the Mohr-Coulomb criterion. The early warning and decision-making output module is equipped with MQTT wireless communication. When the local safety factor falls below a preset threshold, it generates a graded early warning and corresponding quantitative emergency rescue construction parameters, which are then sent to the on-site control platform. The visualization terminal uses WebGL 3D rendering to dynamically display the collapse evolution process, local safety factor cloud map, and time-series curve of the effective passage width of the embankment top.

[0046] In this embodiment, each module is deployed at the edge, and the forecast calculation can be completed independently in a flood rescue environment without network or large computing power. This realizes an integrated closed loop of "risk prediction - intelligent decision-making - mechanized operation". The evolution of collapse risk and rescue construction parameters can be intuitively presented through a visualization terminal, which facilitates on-site command and decision-making and significantly improves the real-time performance and operability of breach rescue.

[0047] Example 5 Based on the above embodiments, taking a typical dike breach emergency rescue scenario as an example, using the actual geological stratification information and geometric dimensions of the dike near the breach as a prototype, the three-dimensional computational domain of the breach edge is set as a cuboid region centered on the breach, with a grid resolution of 1 meter × 1 meter × 0.5 meters. Global Navigation Satellite System displacement gauges are deployed on the dike top surface along the dike axis and perpendicular to the dike axis. Inclinometers are deployed along the depth direction inside the dike body. Pore water pressure gauges are deployed in potential piping areas and at the dike toe. Rolling water level forecasts for a preset future time period are received from upstream hydrological stations via wireless communication.

[0048] The collected discrete data is interpolated into a three-dimensional grid domain using Kriging space. Static equilibrium iterative deduction is then performed using the Duncan-Zhang soil constitutive model to reconstruct the three-dimensional state field at the current moment. After reconstruction, the momentum residuals are used as the basis for the analysis. Verify data quality when the overall mean is greater than Data is collected again for the region with the largest residual and re-interpolated.

[0049] To train the spectrum-adaptive physically constrained Fourier neural operator model, a three-dimensional fluid-structure interaction numerical model was established based on actual geological stratification and geometric dimensions. The soil was modeled using the Mohr-Coulomb constitutive model, and the water flow was modeled using the incompressible Newtonian fluid assumption. A global parametric scan was performed on the inlet velocity (3–10 m / s), water level fluctuation curves (various typical flood hydrographs), effective cohesion (10–40 kPa), effective internal friction angle (15°–35°), piping density, and dike head geometry. Batch processing generated no fewer than 200,000 training samples. Each sample included a displacement field, stress tensor field, pore water pressure field, damage field, and a local safety factor field calculated from the simulated ground truth.

[0050] The model uses a 4-layer Fourier neural operator as its backbone, with the initial state field as input. With boundary condition coding Output the state field increment at a single time step. Configure the number of frequency bands during training. Competition intensity coefficient Moving average attenuation rate Benchmark weights , , Safety factor loss weight The network was trained for 500 epochs. After training, knowledge distillation was used to compress the 4-layer network into 2 layers, and then OpenVINO was used to perform FP16 half-precision quantization. The network was deployed on a Jetson AGX Orin edge device. After optimization, the single complete prediction inference time was less than 100ms, and the single-step inference time was reduced from 12ms to 2.8ms.

[0051] In the inference phase, the current three-dimensional state field and hydrological boundary conditions are input into the model, and time-by-time inference is performed using error-corrected autoregression. Time step The total prediction time is 40 minutes, with a total of 240 autoregressive iterations; each step adds an error correction term and is subject to Lyapunov stability constraints, with the correction step size being [missing information]. The system can predict a 40-minute timeframe sequence in approximately 1 to 2 seconds. After obtaining the three-dimensional state field sequence, it uses time-coupled failure surface evolution tracking to calculate the local safety factor grid by grid. The time smoothing coefficient and parameters are set according to Example 3, forming a local safety factor field covering all future moments. Subsequently, it outputs a three-level warning based on the prediction confidence and the local safety factor range: when the local safety factor is in the range of [1.0, 1.05~1.20) and the confidence is greater than 0.7, a yellow warning is issued to remind the user to prepare reinforcement materials and pre-position anchor points; when it drops to [0.8, 1.0), an orange warning is issued to immediately execute the dike slope reduction and reinforcement, and restrict equipment access; when it is below 0.8, a red warning is issued to order the evacuation of personnel and equipment and initiate the emergency anchoring dragging procedure. At the same time, it automatically outputs quantitative construction parameters such as the reinforcement location and earthwork volume, the dike slope reduction depth, and the coordinates of the equipment anchor points, and sends them to the on-site control platform and the multi-functional emergency rescue equipment auxiliary control system via MQTT for direct execution. The system uses a 10-minute rolling cycle to continuously incorporate the latest monitoring data and re-compile predictions for the set time period, enabling 24 / 7 dynamic tracking of breach and collapse risks.

[0052] Therefore, this invention can still autonomously complete all prediction calculations even in extreme environments where floods cause base station interruptions and there is no fiber optic network. It can output prediction results and construction parameters that meet the real-time decision-making needs of the disaster relief site with a response time of seconds. It achieves high-precision advanced prediction that is constrained by physical laws, interpretable in frequency band, and stable and non-divergent, effectively ensuring the safety of personnel working on the dike and disaster relief equipment.

[0053] Example 6 Based on the above embodiments, this invention will be further described in detail using a real-world scenario of emergency repair of a breach in a main stream dike in a river basin as an example. In this instance, the dike breached due to an above-standard flood, with an initial breach width of approximately 42 meters. The maximum measured flow velocity at the breach reached 9.2 m / s, and severe erosion occurred at the dike toe. Localized rockfalls and small-scale landslides continued to occur on both sides of the dike head. The emergency repair work area was less than 10 meters from the edge of the breach, posing a risk of secondary collapse to personnel and equipment. The real-time dike breach edge collapse prediction system described in this invention was used on-site to provide early warning and support for emergency repair decision-making.

[0054] Step 1: Multi-source monitoring data acquisition and three-dimensional state field reconstruction like Figure 3As shown, multi-source monitoring equipment was deployed at the dike heads on both sides of the breach and within the potential collapse area. Specifically, a GNSS displacement meter was installed every 5m along the dike axis and every 3m perpendicular to the dike axis on the dike top surface to collect real-time displacement vectors of the dike top surface; an inclinometer borehole was drilled every 8m along the dike body, with inclinometer probes installed at 0.5m intervals inside the borehole to acquire the horizontal displacement sequence of the soil along the depth direction; pore water pressure gauges were drilled and installed in the dike toe scour area and potential piping development points to collect spatial distribution data of pore water pressure; simultaneously, the water level and flow velocity process lines for the next 40 minutes were received every 5 minutes from the upstream hydrological station via an emergency communication link.

[0055] The aforementioned discrete monitoring data is synchronously transmitted to the field state reconstruction module, where the Kriging space interpolation algorithm is used to map the discrete data to a three-dimensional computational domain. The computational domain has its origin at the breach center, a length of 200m along the dike axis, a width of 80m perpendicular to the dike axis, and a vertical depth of 30m, with a grid resolution of 1m × 1m × 0.5m. After interpolation, static equilibrium iterative deduction is performed using the Duncan-Zhang soil constitutive model to reconstruct the three-dimensional state field at the current moment, expressed as: In the formula, Three-dimensional spatial coordinates; for The soil displacement vector field at time t; for The soil stress tensor field at time t; for The pore water pressure field at any given moment; for The soil damage variable field at time t; This refers to the current moment.

[0056] Among them, soil damage variable field D is a scalar field with a value range of [0,1], representing the degree of deterioration of soil materials: D=0 corresponds to intact soil, and D=1 corresponds to complete failure.

[0057] The initial damage variables are determined by combining the static equilibrium derivation results with the initial equivalent plastic strain distribution; the evolution of the damage variables over time during the prediction stage is output by the SA-PC-FNO model, reflecting the coupling effect of water flow scouring, stress redistribution and material degradation.

[0058] After reconstruction, perform physical consistency data quality verification and calculate the momentum residuals of all grid points in the global domain. The formula is: In the formula, For spatial points Soil density at the location; It is the vector of gravitational acceleration; For spatial points The stress tensor obtained from reconstruction; Represents the divergence operator; Represents the norm.

[0059] In this example, the soil density is taken according to geological stratification, with 1920 kg / m³ for the silty clay layer. 3 The sand and gravel layer is taken at 2080 kg / m³. 3 When the global mean of the momentum residual is greater than a preset threshold... At that time, the residual peak area is automatically marked as a low data confidence area, triggering the GNSS displacement gauge and pore water pressure gauge sampling frequency in that area to be increased from 1Hz to 2Hz. After supplementing the collected data, interpolation and reconstruction are re-executed to eliminate the interference of abnormal data on subsequent predictions. In this example, the initial reconstruction residual mean value across the entire domain is 32Pa, which is lower than the threshold, so it directly enters the subsequent prediction process.

[0060] Step 2: Spectrum-Adaptive Physically Constrained Fourier Neural Operator Autoregressive Prediction The current three-dimensional state field and the hydrological boundary condition feature vector for the next 40 minutes, which is encoded by time convolution, are input into the spectrum adaptive physical constraint Fourier neural operator (SA-PC-FNO) model deployed in the edge inference module. Through error correction autoregressive iteration, the model is deduced time-by-time and outputs a predicted sequence of the three-dimensional state field for a set time period.

[0061] In this example, the input to the temporal convolutional encoding is the water level process line and flow velocity process line for the next 40 minutes, with a sampling interval of 10 seconds and a sequence length of 240.

[0062] The encoding network consists of two one-dimensional convolutional layers: the first layer has a kernel size of 5, a stride of 2, and 16 output channels; the second layer has a kernel size of 3, a stride of 2, and 32 output channels; finally, global average pooling is applied to output a boundary condition feature vector with a dimension of 32.

[0063] After the feature vector is broadcast to the three-dimensional spatial grid, it is concatenated with the initial state field in the channel dimension to form an input tensor with 36 channels, which is then fed into a 4-layer Fourier neural operator backbone network.

[0064] like Figure 4 As shown, the SA-PC-FNO model in this example uses a 4-layer Fourier neural operator backbone network, with a physically guided spatial attention module embedded after each Fourier layer. This module, in addition to channel-dimensional global average pooling and global max pooling, introduces the predictive stress tensor divergence norm. As the physical attention signal, it is converted into a spatial attention weight map by a 7×7×7 3D convolution and sigmoid activation, expressed as follows: In the formula, The feature map output by the Fourier layer; Global average pooling for channel dimension; Global max pooling for channel dimension; For spatial points Predicted stress tensor at the location; This indicates a channel splicing operation; These are the kernel weights; This is a convolution operation; This is the Sigmoid activation function.

[0065] Each Fourier neural operator layer contains two branches: a Fourier spectral layer and a spatial convolutional layer. The input feature map undergoes a Fourier transform to enter the frequency domain, retaining 16×16×8 patterns (corresponding to the three spatial dimensions of x, y, and z), and then undergoes a spectral transform using a learnable complex-valued weight matrix, followed by an inverse transform back to the spatial domain. Simultaneously, the input feature map is processed by a 3×3×3 spatial convolution. The outputs of the two branches are summed element-wise and then connected to a GELU activation function to form the output of a Fourier layer.

[0066] In this example, each Fourier layer has 32 channels (width); the input layer uses a 1×1×1 convolution to increase the dimensionality of the 36-channel input, which is concatenated with boundary condition encoding, to 32 channels; the output layer uses a 1×1×1 convolution to reduce the dimensionality back to 4 channels (displacement field, stress field, pore water pressure field, and damage field). Residual connections are set between each Fourier layer, that is, the input of the (l+1)th layer is the sum of the residuals between the output of the 1st layer and the input of the 1st layer.

[0067] This attention mechanism enables the model to adaptively focus on high-risk areas of force imbalance, such as scour pits at the embankment toe and piping points, thereby improving the prediction accuracy of local collapse areas.

[0068] like Figure 5 As shown, the model training phase employs a spectrum-adaptive physical constraint loss function, and the total loss expression is: In the formula, For data-driven loss terms; This represents the total number of physical constraint categories. In this example, we take 3, corresponding to the three categories of constraints: conservation of momentum, conservation of mass, and collapse criticality criterion. This represents the total number of frequency bands; in this example, it is set to 16. This refers to the physical constraint category number; Frequency band number; For a specific moment; For the first Frequency characterization of each frequency band; for Time of the first Physically constrained residuals in frequency band Fourier coefficients at the location; for Time of the first Class constraints in the first Adaptive weighting for each frequency band; This represents the L2 norm.

[0069] The expression for the data-driven loss term, which synchronously fits the true value of the state field and the true value of the local safety factor, is as follows: In the formula, This represents the total number of spatial grid points in a single training batch. For grid point numbers; For the first The coordinates of each spatial grid point; and The first The predicted state field vector and the true state field vector at each spatial grid point; and They are respectively Time of the first The predicted local safety factor and the true local safety factor at each spatial grid point; The local safety factor loss weighting coefficient is set to 10 in this example.

[0070] The residuals for the three types of physical constraints are defined as follows: Momentum conservation residual: Mass conservation residual: Collapse Critical Criterion Residual: In the formula, for Time and Space Point The velocity vector of the soil skeleton; for Time and Space Point Stress tensor at the point; It is a linear rectification function.

[0071] The adaptive weights for each frequency band are determined using a competitive normalization mechanism based on the frequency band spectral energy, and the expression is as follows: In the formula, For the first Baseline weights for class constraints; This is the competition intensity coefficient, which is set to 2.0 in this example; For the first Class constraints in the first Spectral energy of each frequency band; This is the physical constraint category number in the summation index.

[0072] The frequency band spectral energy is updated using an exponential moving average according to the following formula: In the formula, The moving average decay rate is set to 0.1 in this example; For time step.

[0073] In this example, the benchmark weights corresponding to the conservation of momentum, conservation of mass, and collapse criticality criterion are respectively taken as follows: , , This loss mechanism enables the model to automatically strengthen momentum conservation constraints in the high-frequency band to capture abrupt stress concentration zones, strengthen mass conservation constraints in the low-frequency band to prevent abnormal volume deformation, and strengthen collapse criterion constraints in the mid-frequency band to accurately calibrate shear bands, thus achieving frequency band-level decoupling of physical constraints.

[0074] The inference phase employs error-corrected autoregressive iteration with a set time step. The predicted total duration is 40 minutes, with a total of 240 iterations. In each iteration, the... The three-dimensional state field at time t is calculated using the following formula: In the formula, for The increment of the state field output by the Fourier neural operator model at each time step; for The error correction term at time step actively corrects the prediction result towards satisfying the physical constraints; its expression is: In the formula, To correct the step size; For the first Weights of physical constraints; Represents the state field vector in three dimensions Find the gradient.

[0075] Correction step size Subject to Lyapunov stability constraints: Let the energy function be... When the correction step size When the exponential decay condition is satisfied The upper limit of the correction step size is determined by the following formula: In the formula, The expected error decay rate is set to 0.01 in this example; is the Lipschitz constant of the Fourier neural operator model; This indicates taking the maximum value. The actual correction step size is... To preserve a safety margin, it is mathematically guaranteed that the 240 steps of autoregressive iteration will not result in error accumulation and divergence.

[0076] The model compresses the 4-layer backbone network into 2 layers through knowledge distillation, and then performs FP16 half-precision quantization using OpenVINO, before being deployed on a Jetson AGX Orin edge computing device. In this example, single-step inference takes 2.8ms, and the total time to complete 240 steps of prediction for a set time period is approximately 1.1s, meeting the second-level decision-making requirements at disaster relief sites.

[0077] Step 3: Tracking the evolution of time-coupled failure surfaces and calculating local safety factors Based on the output three-dimensional state field prediction sequence, the local safety factor is calculated time-by-time and grid-by-grid using a time-coupled failure surface evolution tracking algorithm.

[0078] For each spatial grid point at each prediction time, the stress tensor is first decomposed into eigenvalues ​​to obtain the maximum principal stress. With minimum principal stress Subsequently, the optimal unit normal vector of the potential failure surface is searched. Unlike the traditional method of independently searching the static failure surface at each time step, this example introduces a time continuity constraint and a historical damage memory term into the optimization objective, expressed as: In the formula, This refers to the effective normal stress acting on the potential failure surface; This is the time smoothing coefficient; The historical damage memory coefficient; For historical damage memory items; This is the time derivative of the unit normal vector of the potential failure surface.

[0079] The time derivative term is discretized as follows: In the formula, and They are respectively Time and The unit normal vector of the potential destruction surface at any given time.

[0080] Historical damage memory items are determined by the following formula: In the formula, To remember the window length, this example uses 60; For historical moment sequence numbers; For the time scale used in this example, 10 minutes is taken. for The unit normal vector of the potential damage surface is determined at any given time; for Soil damage variables at any given time.

[0081] In this example, the time smoothing coefficient Angle from the largest interior point With time step Confirmed, historical damage memory coefficient This memory allows the search for damaged surfaces to proactively avoid locations where damage has already occurred, accurately reproducing the continuous evolution path of progressive damage.

[0082] After determining the optimal failure surface normal, the local safety factor is calculated based on the Mohr-Coulomb criterion, expressed as: In the formula, for Time and Space Point Shear strength of the soil at the location; for Time and Space Point The movable shear stress at the potential failure surface is determined by the following formulas: In the formula, For spatial points The effective cohesion of the soil; For spatial points The effective internal friction angle of the soil at the location; for Time and Space Point Predicted pore water pressure at the location; This is the unit normal vector of the potential failure surface.

[0083] In this example, the effective cohesion and effective internal friction angle of the soil were determined by the geological survey of the field. The values ​​were 22 kPa and 21° for the silty clay layer and 8 kPa and 32° for the sand and gravel layer.

[0084] The global safety factor calculation is accelerated by GPU parallelism. The calculation time for a single moment of the full grid is about 180ms, and the total calculation time for 240 prediction moments is about 43s. It can be executed in parallel with the autoregressive prediction process.

[0085] Step 4: Tiered early warning and quantitative emergency response decision output By combining the predicted local safety factor field and the prediction confidence level, a three-level early warning is triggered according to the joint criterion of "safety factor interval × confidence level", and quantitative emergency construction parameters are output simultaneously.

[0086] First, calculate the confidence level of the prediction result, expressed as: In the formula, This represents the total number of physical constraint categories. for Time of the first Total spectral energy across the entire frequency band under class constraints; For the first The baseline spectral energy of class constraints during model training convergence. The confidence index quantifies the physical compliance of current prediction results, providing a reliable basis for early warning grading.

[0087] In this example, a preset threshold is used. The triggering rules and corresponding response plans for Level 3 early warnings are as follows: Yellow alert: When the local safety level is met. And the confidence level is satisfied The system was triggered at the time. During this emergency rescue operation, 12 minutes after the initial prediction, the system identified that the safety factor of a local area 6m from the edge of the breach on the left side of the dike had dropped to 1.06, corresponding to a confidence level of 0.82. It then issued a yellow warning and simultaneously output the list of reinforcement materials for the dike and the coordinates of the anchoring pre-positioning for that area, prompting the rescue team to prepare materials in advance.

[0088] Orange alert: When the local safety level is met The alert was triggered at the specified time. It was predicted that by the 26th minute, the local safety factor in the aforementioned area would drop to 0.93, and the system automatically upgraded to an orange alert, outputting a pre-slope reduction depth of 1.2m at the embankment head and an estimated earthwork volume of approximately 145m³ for the emergency embankment reinforcement. 3 The construction parameters, such as the precise coordinates of the equipment anchor points, were obtained, and the site was instructed to immediately carry out slope reduction and emergency construction of the embankment head, while restricting the entry of heavy equipment into the area.

[0089] Red Alert: When the local safety level is met The system was triggered in a timely manner, simultaneously outputting instructions for personnel and equipment to evacuate the area and for emergency anchoring to be activated. Thanks to timely reinforcement measures implemented during this emergency response, the minimum safety factor in the area remained at 0.88, and a red alert was not triggered.

[0090] The system uses a 10-minute rolling prediction cycle, incorporating the latest monitoring data each cycle to re-predict the set time period, dynamically updating risk distribution and response parameters to achieve 24 / 7 dynamic tracking of breach and collapse risks. During this emergency rescue operation, the system identified the risk of localized collapse at the levee head 21 minutes in advance and output a quantitative reinforcement plan. After the on-site reinforcement was completed according to instructions, the safety factor of the area rose to 1.17, successfully avoiding the risk of levee head collapse and equipment falling into the river.

[0091] Model Training and System Deployment Instructions To train the SA-PC-FNO model used in this example, a three-dimensional fluid-structure coupled numerical model was established based on the actual geological stratification and cross-sectional morphology of the levee. The coupled Eulerian-Lagrange method was used for solution, the soil was assumed to be based on the Mohr-Coulomb constitutive model, and the water flow was assumed to be an incompressible Newtonian fluid. Full parametric scanning was performed on the inlet velocity (3-10 m / s, interval 0.5 m / s), five typical flood hydrographs, effective soil cohesion (10-40 kPa), effective internal friction angle (15°-35°), piping density (0-3 per meter), and levee head geometry (original slope, pre-slope reduction of 30°, 45°). A total of 11,520 sets of high-fidelity numerical simulations were completed. Each set output displacement field, stress field, pore water pressure field, and damage field data every 10 seconds for 40 minutes, and the true value of the local safety factor at the corresponding time was calculated simultaneously. Training samples were generated by randomly selecting 40-minute segments from different start times in the simulated sequence, resulting in a total of 220,000 valid training samples. (See Table 1 for details.) Table 1. Parametric scanning table for generating training samples for the 3D fluid-structure interaction numerical model.

[0092] The model was trained using the Adam optimizer with an initial learning rate of 1×10⁻⁶. -3 The model was trained on a single NVIDIA H100 GPU for 500 epochs with a batch size of 64, taking approximately 76 hours in total. After training, the model's displacement field relative L2 error on the test set was 2.7%, and the safety factor prediction error was 4.1%, representing reductions of 16% and 12% respectively compared to the fixed-weight physical constraint scheme. Under the extreme flow velocity extrapolation condition of 9.2 m / s, the prediction results still fully conformed to the basic laws of soil mechanics, with no non-physical distortions observed.

[0093] The hardware configuration for deploying a real-time prediction system for the edge collapse of a dike breach in this example is as follows: Multi-source data acquisition module: integrates GNSS receiving unit, inclinometer acquisition unit, pore water pressure acquisition unit and hydrological data emergency transmission unit, and synchronously acquires multi-source monitoring data at 1Hz; On-site state reconstruction module: Equipped with a high-performance edge server, with a built-in data quality verification submodule, running spatial interpolation and static deduction programs, a single state reconstruction takes about 7 seconds; Edge inference module: Employs a Jetson AGX Orin embedded device to deploy a lightweight SA-PC-FNO model and perform error-corrected autoregressive prediction calculations; Real-time assessment module for collapse critical value: Based on the CUDA parallel computing framework, runtime coupling of failure surface evolution tracking and local safety factor calculation; Early warning and decision output module: Equipped with an MQTT wireless communication unit, it supports the issuance of structured early warning instructions and construction parameters to the on-site management platform and the emergency equipment control system; Visualization terminal: Adopting a rugged industrial tablet, it uses WebGL 3D rendering to display the collapse evolution process, local safety factor cloud map and time series curve of effective passage width on the top of the embankment in real time.

[0094] The above practical applications demonstrate that this invention can operate independently in field emergency rescue environments without base stations or fiber optic cables, improving the computational efficiency of high-fidelity three-dimensional fluid-structure interaction simulation by three orders of magnitude. At the same time, through mechanisms such as spectrum-adaptive physical constraints, Lyapunov stable autoregression, and time-coupled failure surface tracking, it ensures the physical rationality and long-term stability of predictions under extreme conditions, realizing second-level advance prediction of breach edge collapse risks and quantitative implementation of emergency rescue decisions, providing strong technical support for the safety of personnel and equipment in dike breach rescue.

[0095] Those skilled in the art will understand that the above embodiments can be modified in form and detail in practical applications without departing from the spirit and scope of the invention.

Claims

1. A method for real-time prediction of levee breach edge collapse, characterized in that, Includes the following steps: S1. Obtain multi-source monitoring data at the breach site, perform spatial interpolation on the discrete monitoring data, and conduct static equilibrium deduction based on the soil constitutive model to reconstruct the three-dimensional state field at the current moment. S2. Input the current three-dimensional state field and the hydrological boundary conditions within a set future time period into the trained spectrum adaptive physical constraint Fourier neural operator model. Through error correction autoregression iteration, the model is deduced time by time and outputs a three-dimensional state field prediction sequence covering the set future time period. S3. Based on the predicted three-dimensional stress field, a time-coupled failure surface evolution tracking method is adopted to apply time continuity constraints to the potential failure surface at each time step, to determine the potential failure surface of each spatial point at each prediction time, and to calculate the local safety factor of each spatial point in real time according to the Mohr-Coulomb criterion. S4. When the local safety factor is lower than the preset threshold, a graded warning is issued and the corresponding quantitative emergency rescue construction parameters are output.

2. The method for real-time prediction of dike breach edge collapse as described in claim 1, characterized in that, The training loss used during training of the Fourier neural operator model Data-driven loss terms The training loss is composed of a spectrum-adaptive physical constraint loss term, which decomposes the residuals of three types of physical constraints—momentum conservation, mass conservation, and collapse criticality criterion—in the Fourier frequency domain by frequency band, and adaptively allocates the weights of each constraint within each frequency band using a competitive mechanism. The expression is: In the formula, For data-driven loss terms; The total number of physical constraint categories, including at least three categories: momentum conservation, mass conservation, and collapse criticality criterion. This represents the total number of frequency bands. This refers to the physical constraint category number; Frequency band number; For a specific moment; For the first Frequency characterization of each frequency band; for Time of the first Physically constrained residuals in frequency band Fourier coefficients at the location; for Time of the first Class constraints in the first Adaptive weighting for each frequency band; This represents the L2 norm.

3. The method for real-time prediction of dike breach edge collapse as described in claim 2, characterized in that, The data-driven loss term Determine using the following formula: In the formula, This represents the total number of spatial grid points in a single training batch. For grid point numbers; For the first The coordinates of each spatial grid point; and The first The predicted state field vector and the true state field vector at each spatial grid point; and They are respectively Time of the first Predicted local safety factor and true local safety factor at each spatial grid point; This is the weighting coefficient for the local safety factor loss. The residuals of the three types of physical constraints—momentum conservation, mass conservation, and collapse critical criterion—are determined by the following formulas: In the formula, , and They are respectively Time of the first Momentum conservation residuals, mass conservation residuals, and collapse critical criterion residuals at each spatial grid point; For spatial points The density of the soil at that location; for Time and Space Point The velocity vector of the soil skeleton; for Time and Space Point Stress tensor at the point; Represents the divergence operator; It is the vector of gravitational acceleration; It is a linear rectified function; for Time of the first The predicted local safety factor for each spatial grid point is calculated based on the predicted stress field.

4. The method for real-time prediction of dike breach edge collapse as described in claim 2, characterized in that, The first Class constraints in the first Adaptive weighting of each frequency band The competitive normalization mechanism based on frequency band spectral energy is used, and the result is determined according to the following formula: In the formula, For the first Baseline weights for class constraints; This is the competition intensity coefficient; For the first Class constraints in the first Spectral energy of each frequency band; To sum the physical constraint category numbers in the index; The frequency band spectrum energy Update the exponential moving average as follows: In the formula, The moving average decay rate; For time step; for Time of the first Physically constrained residuals in frequency band Fourier coefficients at the location.

5. The method for real-time prediction of dike breach edge collapse as described in claim 1, characterized in that, In step S2, during the error correction autoregressive iteration, the first... The three-dimensional state field at time t is determined by the following formula: In the formula, for The three-dimensional state field at any given time; for The three-dimensional state field at any given time; for The state field increment output by the Fourier neural operator model at time t; for The time error correction term is determined by the following formula: In the formula, To correct the step size; This represents the total number of physical constraint categories. For the first Weights of physical constraints; for Time of the first Physically constrained residuals; Represents the state field vector in three dimensions Find the gradient.

6. The method for real-time prediction of levee breach edge collapse as described in claim 5, characterized in that, The correction step size Satisfying the Lyapunov stability constraint, the Lyapunov stability constraint is: Let the energy function be... When the correction step size When the exponential decay condition is satisfied The upper limit of the correction step size Determine using the following formula: In the formula, The expected error decay rate; is the Lipschitz constant of the Fourier neural operator model; For the first Weights of physical constraints; For the first The gradient of the physical constraint residual with respect to the three-dimensional state field; Represents the L2 norm; This indicates taking the maximum value; the correction step size Take as .

7. The method for real-time prediction of dike breach edge collapse as described in claim 1, characterized in that, The Fourier neural operator model embeds a physically guided spatial attention module between each Fourier layer. This module, based on channel-dimensional global average pooling and channel-dimensional global max pooling, introduces the predicted stress tensor divergence norm as the physical attention signal, generating a spatial attention weight map for each spatial point. Determine using the following formula: In the formula, The feature map output by the Fourier layer in the Fourier neural operator model; and These are channel-dimensional global average pooling and channel-dimensional global max pooling, respectively. For spatial points Predicted stress tensor at the location; To predict the divergence of the stress tensor; Represents the norm; This indicates a channel splicing operation; These are the kernel weights; This is a convolution operation; This is the Sigmoid activation function.

8. The method for real-time prediction of dike breach edge collapse as described in claim 1, characterized in that, The local safety factor in step S3 Calculate using the following formula: In the formula, for Time and Space Point Shear strength of the soil at the location for Time and Space Point The movable shear stress at the potential failure surface is determined by the following formulas: In the formula, For spatial points The effective cohesion of the soil; For spatial points The effective internal friction angle of the soil at the location; for Time and Space Point Predicted stress tensor at the location; for Time and Space Point Predicted pore water pressure at the location; The unit normal vector of the potential failure surface; The potential failure surface is determined by time-coupled failure surface evolution tracking, and its unit normal vector is... Optimize as follows: In the formula, This refers to the effective normal stress acting on the potential failure surface; This is the time smoothing coefficient; The historical damage memory coefficient; For historical damage memory items; The time derivative of the unit normal vector of the potential failure surface is discretized by the following formula: In the formula, and They are respectively Time and The potential destructive surface normal vector at any given moment; For time step; The historical damage memory item Determine using the following formula: In the formula, To store the length of the memory window; For historical moment sequence numbers; For the time scale of memory; for The unit normal vector of the potential damage surface is determined at any given time; for Soil damage variables at any given time.

9. The method for real-time prediction of dike breach edge collapse as described in claim 1, characterized in that, After reconstructing the three-dimensional state field in step S1, the physical consistency data quality of the three-dimensional state field is verified. The verification uses momentum residuals. Determine using the following formula: In the formula, For spatial points The density of the soil at that location; It is the vector of gravitational acceleration; For spatial points The stress tensor obtained from reconstruction; Represents the divergence operator; Represents the norm; When the global mean of the momentum residual Greater than the preset residual threshold When the area with the largest residual is marked as the area with low data confidence, the sampling frequency of the monitoring data in that area is increased, and the data is supplemented and then re-interpolated. In step S4, the confidence level of the prediction result is calculated. Determine using the following formula: In the formula, This represents the total number of physical constraint categories. for Time of the first Physically constrained full-band total spectral energy; For the first The baseline spectral energy of physical constraints during the training convergence period; The tiered early warning is triggered by a joint criterion of local safety factor range and confidence level. and A yellow alert is issued and a list of head-wrapping reinforcement materials and anchorage pre-positioning coordinates are output. An orange alert is issued and the pre-slope reduction depth of the dike head, the volume of earth and stone for emergency construction of the dike head, and the coordinates of the equipment anchoring points are output. A red alert is issued and instructions are sent to evacuate personnel and equipment from the designated area and to activate emergency anchoring; among other things, This is a preset threshold.

10. A real-time prediction system for the collapse at the edge of a dike breach, used to implement the real-time prediction method for the collapse at the edge of a dike breach as described in any one of claims 1 to 9, characterized in that, include: Multi-source data acquisition module, used to acquire multi-source monitoring data; The field state reconstruction module is used to perform spatial interpolation on discrete monitoring data and static equilibrium deduction based on the soil constitutive model to reconstruct the three-dimensional state field at the current moment. The field state reconstruction module is equipped with a data quality verification submodule, which is used to perform physical consistency verification on the reconstructed three-dimensional state field based on momentum residuals. The edge reasoning module is internally deployed with a trained spectrum adaptive physical constraint Fourier neural operator model, which is used to receive the three-dimensional state field and hydrological boundary conditions, and output a three-dimensional state field prediction sequence covering a future set time period through error correction autoregression iterative output. The real-time assessment module for collapse critical values ​​is used to determine potential failure surfaces based on the predicted three-dimensional stress field by employing time-coupled failure surface evolution tracking, and to calculate the local safety factor for each spatial point according to the Mohr-Coulomb criterion. The early warning and decision output module is used to generate graded early warnings and corresponding quantitative emergency rescue construction parameters when the local safety factor is lower than the preset threshold, and send them to the on-site control platform. A visualization terminal is used to display the collapse evolution process, local safety factor cloud map, and the curve of change in the effective passage width of the embankment top in real time.

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