Slope overall-local collaborative instability prediction method and system based on multi-ground-based radar

Abstract

This application discloses a method and system for predicting overall-local coordinated slope instability based on multiple ground-based radars. At least three ground-based radars are deployed in the stable zone of the slope to collect echo signals. The deformation data along the line-of-sight direction is calculated and fused to obtain a three-dimensional displacement field across the entire slope. Based on the displacement field, the overall and local deformation characteristics of unstable rocks are extracted, and predictions of overall instability trends and rockfall states are made accordingly. The overall-local coupling relationship is quantified using an correlation matrix to determine whether to activate a coordinated early warning system. Sliding surface parameters and safety factors are calculated to simulate the trajectory of the unstable body, and the rockfall motion equations are numerically solved to simulate the fall trajectory. The two types of trajectories, along with the overall and local deformation determination results, generate graded early warning information. This application achieves trajectory-based graded early warning for overall-local coordinated slope instability, improving the accuracy of slope instability prediction.

Description

Technical Field

[0001] This application relates to the field of engineering slope safety monitoring and disaster early warning technology, specifically to a method and system for predicting overall-local coordinated instability of slopes based on multi-ground radar, which is applicable to real-time stability monitoring and safety control of high slopes during construction and operation. Background Technology

[0002] High slope instability disasters are characterized by their high degree of concealment, destructive power, and complex causes. Existing monitoring methods have the following main shortcomings:

[0003] (1) Point sensors (such as GNSS, inclinometers, etc.) can only acquire local deformation information and cannot fully reflect the instability path of the slope system;

[0004] (2) Alarm mechanisms based on fixed thresholds have a high false alarm rate and cannot identify precursors to unstable critical states;

[0005] (3) Numerical simulation methods are difficult to integrate monitoring data in real time and are insufficient for dynamic characterization of local-global coupling instability processes.

[0006] Ground-based synthetic aperture radar has advantages such as non-contact operation, high resolution, and all-weather operation, enabling continuous monitoring of large-scale slope surfaces. However, existing technologies lack a systematic method for coordinating the prediction of overall instability trends and the risk of local rockfalls. Summary of the Invention

[0007] To address the shortcomings of existing technologies, this application proposes a method and system for predicting overall and local slope instability based on multi-ground radar, which improves the accuracy of slope instability prediction.

[0008] The technical solution provided in this application is as follows:

[0009] In a first aspect, this application provides a method for predicting overall-local coordinated instability of slopes based on multi-ground radar, comprising the following steps:

[0010] S1. Deployment and data acquisition of multiple ground-based radars: Deploy at least three ground-based radars in the stable area outside the deformation zone on the front of the slope to build a synchronous monitoring network covering the entire slope area and collect the surface echo signal of the slope in real time according to the preset sampling interval.

[0011] S2. Three-dimensional displacement inversion: Based on the echo signal of the slope surface, obtain the deformation data of the line of sight of the ground radar in various locations; fuse the deformation data of the line of sight of the ground radar in various locations, and invert the three-dimensional displacement vector of any monitoring point on the slope surface through the observation equation and the weighted least squares estimation method to obtain the three-dimensional displacement field of the entire slope.

[0012] S3. Extraction of overall and local deformation features of slope: Based on the three-dimensional displacement field obtained in step S2, extract the overall deformation features and local deformation features of unstable rocks of the slope.

[0013] S4. Overall-local coordinated instability prediction: Based on the overall deformation characteristics of the slope and the deformation characteristics of local dangerous rocks, the overall instability trend of the slope and the state of dangerous rock falling are predicted. The coupling relationship between the overall deformation of each area of ​​the slope and the risk of falling of each dangerous rock is quantified by the correlation matrix to determine whether to activate the overall-local coordinated early warning.

[0014] In one possible implementation, in step S2, the observation equation is:

[0015] ;

[0016] in, For the first Line-of-sight deformation measured by Taiwan radar For the first Taiwan radar to monitoring point The unit line-of-sight vector, ; Monitoring point P is located at The true displacement components in the direction, The observed noise follows a mean of 0 and a variance of . The normal distribution;

[0017] The solution formula for the weighted least squares estimation method is as follows:

[0018] ;

[0019] in, For the estimated monitoring points Three-dimensional displacement vector The optimal value; It is a 3×3 geometric matrix, where each row represents a radar to a monitoring point. The unit line-of-sight vector; For the observed data vector, , The weight matrix is ​​constructed from the standard deviation of the observation error estimated by the radar coherence coefficient.

[0020] In one possible implementation, in step S2, the weight matrix Standard deviation of observation error of a single radar Through radar coherence coefficient The estimated formula is: ;in, This refers to the radar wavelength.

[0021] In one possible implementation, in step S3, the overall deformation characteristics of the slope include the average displacement rate of each region of the slope. Displacement acceleration Deformation uniformity coefficient The local deformation features of the unstable rock include the coordinates of the rock's center. Displacement rate and rotation angle θ.

[0022] In one possible implementation, in step S3, the slope is divided into three regions—upper, middle, and lower—according to its height. The average displacement rate, displacement acceleration, and deformation uniformity coefficient of each region are calculated using the following formulas: , , ;in, The number of monitoring points in the area. For the first in the region Displacement rate at each monitoring point , The first and the The average regional displacement rate over a time interval.

[0023] The dangerous rock was identified through radar image grayscale features, and its displacement rate was determined by the formula... calculate, For dangerous rocks at time intervals Deformation (displacement) within. The radar sampling interval is given by the rotation angle θ, which is calculated by matching the contours of the dangerous rocks at adjacent time points.

[0024] In one possible implementation, in step S4, an ARIMA time series model is used to predict the overall instability trend of the slope. The model parameters are optimized using the AIC criterion to obtain displacement prediction data (including displacement prediction curves and displacement acceleration prediction values) for each region of the slope. If the displacement acceleration prediction value... and This triggered an overall instability warning; among which The second displacement acceleration threshold, This is the threshold value for the uniformity coefficient of regional deformation.

[0025] A CNN classification model is constructed to predict the falling state of dangerous rocks. The model takes the displacement rate, rotation angle and overall acceleration of the region as input features and outputs the judgment results of three types of falling states: stable, potential falling and imminent falling.

[0026] The correlation matrix M is an m×n two-dimensional matrix, where m is the number of slope area divisions and n is the number of identified dangerous rocks. The matrix element M(i,j) is calculated using the following formula: ;in, The covariance between the displacement acceleration of region i and the displacement rate of the j-th unstable rock. Let be the standard deviation of the displacement acceleration in the i-th region. Let be the standard deviation of the displacement rate of the j-th unstable rock; if It is determined that there is a strong coupling relationship between the overall deformation of the i-th region and the risk of the j-th dangerous rock falling, and an overall-local coordinated early warning is initiated.

[0027] In one possible implementation, the method further includes: S5, instability trajectory prediction and graded early warning: calculating the slope sliding surface parameters and safety factor, determining whether the slope is unstable, and simulating the overall instability trajectory of the unstable slope; simulating the trajectory of falling rocks by combining the rock motion equation with numerical solution methods; combining the overall slope instability trajectory simulation results and the rock falling trajectory prediction results, and simultaneously making a comprehensive judgment based on the threshold judgment results of the overall slope deformation characteristics and the local rock falling state, generating graded early warning information, and realizing the overall-local coordinated trajectory-based graded early warning of the slope.

[0028] In one possible implementation, in step S5, the sliding surface parameters include cohesion. internal friction angle Normal stress and shear stress Safety factor of sliding surface The calculation formula is: ; Safety factor of sliding surface With preset threshold In comparison, if To determine slope instability, the overall instability trajectory of the slope is simulated using the limit equilibrium theory in conjunction with a three-dimensional terrain model.

[0029] The motion equation of the unstable rock comprehensively considers gravity, air resistance, slope support force and collision effect. The Runge-Kutta method is used to numerically solve the motion equation of the unstable rock to obtain the trajectory of the unstable rock falling.

[0030] In one possible implementation, in step S5, the graded early warning information is a four-level graded early warning, and the specific judgment and output rules are as follows:

[0031] Level 1 warning: If the displacement acceleration in the overall deformation characteristics of the slope If a dangerous rock is determined to fall immediately and the landing point is located within the construction area, output the direction of instability development, the coordinates of the covered area, the landing point of the dangerous rock, and personnel evacuation instructions.

[0032] Level 2 warning: If If a dangerous rock is determined to fall immediately and the landing point is within a preset distance outside the construction area, output the displacement prediction curve, the trajectory diagram of the dangerous rock, and the instruction to strengthen monitoring.

[0033] Level 3 warning: If the deformation uniformity coefficient in the overall deformation characteristics of the slope is... and When a dangerous rock is determined to be a potential falling rock, output a report on the deformation characteristics of the area, monitoring data of the dangerous rock, and instructions for regular inspections.

[0034] Level 4 Warning: If and When all dangerous rocks are determined to be stable, a summary of routine monitoring data is output; among them, The first displacement acceleration threshold, The second displacement acceleration threshold, This is the threshold value for the uniformity coefficient of regional deformation.

[0035] Secondly, this application provides a slope overall-local coordinated instability prediction system based on multi-ground radar. The system is used in the above-mentioned method and includes a data acquisition layer, a data processing layer and a model analysis layer.

[0036] The data acquisition layer includes multiple ground-based radars deployed in the stable area outside the deformation zone on the front of the slope, used to construct a synchronous monitoring network covering the entire slope area, and to collect the slope surface echo signals in real time according to a preset sampling interval.

[0037] The data processing layer obtains deformation data in the line-of-sight direction of various base radars based on the echo signal of the slope surface; it fuses the deformation data in the line-of-sight direction of various base radars, and inverts the three-dimensional displacement vector of any monitoring point on the slope surface through observation equations combined with weighted least squares estimation method to obtain the three-dimensional displacement field of the entire slope.

[0038] The model analysis layer is used to extract the overall deformation characteristics and local rockfall deformation characteristics of the slope based on the three-dimensional displacement field. Based on the overall deformation characteristics and local rockfall deformation characteristics, it predicts the overall instability trend of the slope and the state of rockfall. It also quantifies the coupling relationship between the overall deformation of each area of ​​the slope and the risk of rockfall through the correlation matrix, and determines whether to activate the overall-local coordinated early warning.

[0039] In one possible implementation, the system further includes an early warning application layer, which calculates the slope sliding surface parameters and safety factor, determines whether the slope is unstable, and simulates the overall instability trajectory of the unstable slope; simulates the falling trajectory of the unstable rock by combining the rock motion equation with numerical solution methods; combines the simulation results of the overall slope instability trajectory and the predicted results of the falling rock trajectory, and makes a comprehensive judgment based on the threshold judgment results of the overall slope deformation characteristics and the local falling rock state, to generate graded early warning information, thereby realizing a coordinated trajectory-based graded early warning for the overall and local slope.

[0040] The specific implementation of the second aspect of this application can refer to the implementation of the first aspect, and will not be elaborated here.

[0041] Beneficial effects:

[0042] The method and system for predicting overall and local slope instability based on multi-ground radar provided by this invention overcomes the limitations of traditional slope monitoring and early warning technologies. It achieves full-process coordination, precision, and intelligence in high slope instability prediction and trajectory early warning, significantly improving the reliability, foresight, and practicality of slope safety control. The specific beneficial effects are as follows:

[0043] Multi-radar collaborative inversion significantly improves displacement monitoring accuracy: By deploying at least three ground-based radars in a triangular configuration, fusing deformation data from multiple viewpoints along the line of sight, and combining weighted least squares estimation to invert the three-dimensional displacement field, the radar coherence coefficient is used to optimize the weight matrix, effectively reducing monitoring errors. The three-dimensional displacement identification error is reduced by more than 60% compared to traditional methods, laying a precise data foundation for subsequent feature extraction and predictive analysis.

[0044] The fusion of overall and local features enables accurate prediction of coupled instability: The overall deformation features of the slope and the local deformation features of dangerous rocks are extracted simultaneously. The overall instability trend and the state of dangerous rock falling are accurately predicted by using the ARIMA model and the CNN classification model, respectively. The coupling relationship between the two is then quantified by the correlation matrix. This overcomes the shortcomings of traditional technologies that "emphasize the whole and neglect the local" or provide early warning based on a single indicator. It significantly reduces the false alarm rate and the false alarm rate of early warning, and achieves a scientific judgment of overall and local coordinated instability.

[0045] Multi-factor fusion trajectory simulation enables accurate prediction of landing point and instability path: Based on the Mohr-Coulomb strength criterion and combined with the three-dimensional displacement field calculation of sliding surface parameters, the overall instability trajectory of the slope is accurately simulated; the prediction of the trajectory of falling rocks comprehensively considers gravity, air resistance, slope support force and collision effect, and uses the Runge-Kutta method to numerically solve the motion equations. The landing point prediction error is ≤2m, providing accurate spatial location basis for safety prevention and control.

[0046] Multi-dimensional comprehensive judgment and graded early warning adapted to engineering practice: Combining the dual trajectory results of unstable body and dangerous rock, graded early warning information is generated based on the overall deformation characteristic threshold and the local dangerous rock falling status. The four-level early warning system corresponds to different risk levels and prevention and control instructions, forming a full-process control from routine monitoring to emergency evacuation. The early warning information is highly targeted and practical, perfectly adapting to the actual needs of slope safety management.

[0047] Non-contact, full-area monitoring, suitable for complex engineering scenarios: Relying on the advantages of ground-based radar in non-contact, high resolution and all-weather operation, it can realize continuous and synchronous monitoring of the entire slope area. There is no need to deploy point sensors, avoiding the limitations of complex slope terrain on monitoring equipment. It has a wide monitoring range and fast response speed, and can capture subtle deformation characteristics of the slope in real time and identify the critical signs of instability in advance.

[0048] Overall, this invention constructs a complete technical system of "data acquisition - displacement inversion - feature extraction - collaborative prediction - trajectory early warning", realizing the linkage prediction and trajectory-based early warning of overall instability of high slopes and local rockfalls, which greatly improves the prevention and control capabilities of slope instability disasters and provides reliable technical support for the safe operation of engineering high slopes. Attached Figure Description

[0049] Figure 1 System overall architecture diagram;

[0050] Figure 2 : Block diagram of the global-local collaborative prediction model

[0051] Figure 3 Block diagram of the rockfall prediction model Detailed Implementation

[0052] To enable those skilled in the art to better understand the present application, the technical solution of the present application will be further described in detail below with reference to the embodiments and accompanying drawings.

[0053] Example 1:

[0054] This embodiment proposes a slope overall-local coordinated instability prediction method based on multi-ground radar. By constructing a three-level technical system of "macro-overall prediction - micro-local early warning - coordinated correlation analysis", it can realize the scientific judgment of slope instability trend and the accurate prediction of rockfall trajectory, thereby improving the reliability and foresight of slope safety control.

[0055] The technical solution of this embodiment includes five core components: multi-radar deployment, three-dimensional displacement inversion, feature extraction, collaborative prediction, trajectory simulation, and hierarchical early warning.

[0056] S1. Deployment and data acquisition of multiple ground-based radars:

[0057] In the stable area outside the deformation zone on the front of the slope, at least three (e.g., 3) ground-based radars (e.g., Ku-band radars) are deployed. The coordinates of each radar's working base point are known, and the line-of-sight conditions are good. They are arranged in a triangular pattern to form spatial geometric constraints, constructing a synchronous monitoring network covering the entire slope area. The radar sampling interval is set to... (The range of values ​​is) By acquiring echo signals (raw monitoring data) from the slope surface in real time (e.g., every 2-6 minutes), synchronous three-dimensional displacement monitoring of the entire slope can be achieved. This deployment scheme optimizes the radar position and viewing angle to ensure multi-angle observation of each monitoring point on the slope surface, providing a data foundation for subsequent high-precision three-dimensional displacement inversion.

[0058] S2, Three-dimensional displacement inversion:

[0059] Three ground-based radars simultaneously observed the slope surface monitoring point (inversion point) P from different perspectives, obtaining the corresponding echo signals. The deformation along the radar line-of-sight (LOS) direction was calculated from the echo signals. The LOS deformation data from each ground-based radar were then fused to obtain the three-dimensional displacement vector of monitoring point P. The observation equation is:

[0060] ;

[0061] in, For the first LOS-direction deformation measured by Taiwan radar For the first Taiwan radar to monitoring point The unit line-of-sight vector, Monitoring point P is located at The true displacement components in the direction, The observed noise follows a mean of 0 and a variance of . The normal distribution (Gaussian distribution), that is .

[0062] The solution is obtained using weighted least squares estimation:

[0063] ;

[0064] in, For the estimated monitoring points Three-dimensional displacement vector The optimal value; It is a 3×3 geometric matrix, where each row represents a radar to a monitoring point. The unit line-of-sight vector; For the observed data vector, .

[0065] weight matrix ,in The standard deviation of the observation error of a single radar is given by the radar coherence coefficient. estimate:

[0066] ;

[0067] in, This refers to the radar wavelength.

[0068] The aforementioned three-dimensional displacement inversion model based on weighted least squares overcomes the limitation of a single radar only acquiring one-dimensional deformation information by fusing deformation data from multiple radar LOS, thus reducing the error in three-dimensional displacement inversion. Furthermore, by using radar coherence coefficients to estimate observation error weights, the accuracy of displacement inversion is improved, and the three-dimensional displacement identification error is reduced by more than 60% compared to traditional methods.

[0069] S3. Extraction of overall and local deformation features of slope:

[0070] (1) Overall slope feature extraction: The slope is divided into three regions, upper, middle and lower, according to the slope height, and the average displacement rate of each region is calculated. :

[0071] ;

[0072] in, The number of monitoring points in the area. For the first in the region Displacement rate at each monitoring point.

[0073] Displacement acceleration is a key indicator for determining whether a slope is entering a phase of accelerated deformation and is approaching instability. Calculation of displacement acceleration (average displacement acceleration) is crucial. :

[0074] ;

[0075] in, , The first and the The regional average displacement rate was calculated over a time interval.

[0076] Calculate the deformation uniformity coefficient of the region :

[0077] ;

[0078] when At that time, the concentrated deformation in the determined area was a precursor to overall instability; among them, The threshold value for the uniformity coefficient of regional deformation is an empirical value, such as 0.8.

[0079] (2) Local dangerous rock feature extraction: dangerous rocks are identified based on the grayscale features of radar images. For example, the grayscale features of radar images are used to identify rocks whose grayscale difference with the surrounding area is greater than a preset threshold (e.g., 30). The center coordinates of the dangerous rocks are extracted. Displacement rate and rotation angle The formula for calculating the displacement rate is as follows:

[0080] ;

[0081] in, For dangerous rocks at time intervals Internal deformation, This refers to the radar sampling interval.

[0082] The rotation angle θ is calculated by matching the contours of the dangerous rock at adjacent moments, reflecting the rotation state of the dangerous rock.

[0083] S4. Prediction of overall-local coordinated instability:

[0084] (1) Overall instability prediction: The displacement time series data of each area of ​​the slope are used as input. An ARIMA time series model (AutoRegressive Integrated Moving Average Model) is constructed for the displacement time series data of each area to predict the displacement data of each area. The model expression is as follows:

[0085] ;

[0086] in, For difference operators, for Time-displacement sequence, for Time-displacement sequence, Let be the difference order. For constant terms, Let be the order of the autoregressive term. These are the autoregressive coefficients. , for The random error term at time t, for The random error term at time t, Let the order of the moving average term be denoted by . The moving average coefficient ( ).

[0087] For the difference order in the model The order of the autoregressive term The order of the moving average term Perform initial assignments to prepare for subsequent parameter optimization.

[0088] The model is evaluated using the AIC (Akaike Information Criterion). , , The parameters are iteratively optimized to select the parameter combination that minimizes the AIC value, and the optimal ARIMA time series model for displacement prediction in each region is determined. This ensures the model's fitting accuracy to the temporal variation of slope displacement and lays the foundation for subsequent accurate prediction.

[0089] By substituting the optimized parameters into the model, the displacement sequence of each area of ​​the slope at future times is predicted, and the displacement prediction data of each area of ​​the slope is obtained, that is, the displacement change trend data over time, including displacement prediction curves, displacement acceleration prediction values, etc., realizing the transformation from "historical displacement data analysis" to "future displacement trend prediction", and providing predictive data support for subsequent displacement acceleration calculation.

[0090] Using the unified calculation formula for displacement acceleration from step S3, the average displacement rate of each region is calculated based on the model-predicted future displacement sequence. Then, the predicted future displacement acceleration values ​​for each region are derived from the rate of change of the rate over time. .

[0091] The calculated displacement acceleration prediction value The uniformity coefficient of regional deformation extracted in step S3 With preset threshold , For comparison, if the predicted displacement acceleration value and This triggered an overall instability warning. Among them, The second displacement acceleration threshold is an empirical value, such as 0.5. It represents millimeters per day².

[0092] (2) Prediction of falling rocks: Construct a CNN classification model, whose input feature matrix It is determined by the displacement rate of the dangerous rock. Rotation angle θ and overall acceleration of the region The three core input features are standardized and expanded in dimensionality to construct a two-dimensional matrix, which outputs the probability of the fall state.

[0093] The output feature map of the CNN convolutional layer is calculated as follows:

[0094] ;

[0095] in, For the output feature map located at the th line, number The values ​​of the elements in the column. For activation function, , The circular index variable (representing the first, second, and third cycles respectively) line, number List), For convolution kernel weights, Input feature matrix The Middle line, number The value of the element at the column position. For bias.

[0096] The probabilities of different fall states are obtained based on the output feature map. For example, the normalized probability values ​​obtained after the output feature map is compressed in dimension and weighted by a fully connected layer and a softmax activation layer directly correspond to the probabilities of three fall states: stable, potential fall, and immediate fall.

[0097] The fall state corresponding to the highest probability value is taken as the judgment result.

[0098] (3) Collaborative association analysis: establishing an association matrix ,element Indicates the first Overall deformation of the region and the first Correlation coefficient of risk of falling rocks:

[0099] ;

[0100] in, Let be the covariance between the displacement acceleration of region i and the displacement rate of the j-th unstable rock. For the first Displacement acceleration of the region, For the first The displacement rate of the unstable rock. Let be the standard deviation of the displacement acceleration in the i-th region. Let be the standard deviation of the displacement rate of the j-th unstable rock.

[0101] like If a strong coupling relationship is determined between the whole and its parts, a coordinated early warning system for whole-part collaboration is initiated; among which... The threshold for the preset correlation coefficient is set to an empirical value, such as 0.7.

[0102] This application establishes a collaborative prediction framework for overall slope instability and localized rockfalls, using a correlation matrix. Quantify the coupling relationship between the two. Overcome the shortcomings of existing technologies that "emphasize the whole and neglect the part" or rely on a single indicator for early warning, and achieve linked prediction of overall instability trend and local fall risk.

[0103] In some embodiments, the method further includes: S5, instability trajectory prediction and graded early warning:

[0104] (1) Prediction of overall slope instability trajectory: The potential sliding surface parameters of the slope are calculated based on the Mohr-Coulomb strength criterion. The sliding surface parameters include physical and mechanical parameters reflecting the inherent shear strength of the soil and rock mass, and stress parameters characterizing the real-time stress state of the sliding surface, specifically including cohesion. internal friction angle Normal stress and shear stress Among them, cohesion and internal friction angle The normal stress is an inherent property of the slope soil and rock mass and a core indicator of the soil and rock mass's resistance to shear failure at the sliding surface. Its value can be obtained through engineering geological investigation combined with indoor soil and rock mechanics tests. and shear stress The real-time stress parameters generated at the potential sliding surface of the slope under the action of self-weight, external load and deformation are based on the three-dimensional displacement field of the entire slope obtained by inversion in step S2. The parameters are derived by stress-strain transformation and time sequence analysis of the three-dimensional displacement field data and can be updated in real time with the dynamic deformation of the slope.

[0105] Cohesion internal friction angle Normal stress and shear stress Together, they constitute a complete sliding surface parameter system, which not only reflects the inherent mechanical properties of the slope's soil and rock mass but also the real-time stress state of the sliding surface as the slope deforms. This provides a basis for subsequent calculations of the sliding surface safety factor based on limit equilibrium theory. It provides accurate and comprehensive core input for determining the overall instability of slopes.

[0106] Sliding surface parameters (including cohesion) were calculated based on the Mohr-Coulomb strength criterion. internal friction angle Normal stress and shear stress ), and then calculate the safety factor of the sliding surface. The formula is:

[0107] ;

[0108] in, For cohesion, It is the internal friction angle. For normal stress, This is shear stress.

[0109] The safety factor of the sliding surface is calculated. Then, compare it with the preset safety factor threshold. Comparison; among them Take an empirical value, such as 1.0.

[0110] like If the slope sliding surface is determined to be in a stable / basically stable state, there is no need to start the simulation of the overall slope instability trajectory (instability body movement trajectory); only continuous monitoring of slope deformation is required.

[0111] like The slope is determined to be unstable; if the total resistance force of the sliding surface is less than the total sliding force, the slope has entered an unstable state. The overall slope instability trajectory simulation is immediately initiated to provide accurate data such as the instability trajectory and coverage area for subsequent graded early warning.

[0112] Among them, the simulation of the overall instability trajectory of the slope is combined with a three-dimensional terrain model and realized through the theory of limit equilibrium.

[0113] (2) Prediction of the trajectory of falling rocks: Considering gravity, air resistance, slope support force and collision effect, the equation of motion of the falling rocks is:

[0114] ;

[0115] in, The resultant acceleration vector of the dangerous rock. It is the acceleration due to gravity. The slope angle is... air density, The air drag coefficient is 0.47 for a sphere. The windward area of ​​the dangerous rock. For the quality of dangerous rocks, The relative velocity of the dangerous rock. It is a unit vector in the direction of velocity. The friction coefficient is 0.6 (taken as 0.6 between rocks). Normal velocity, Let be the radius of curvature of the collision. It is the unit vector along the tangent of the slope.

[0116] Solve the equations of motion for the unstable rock to obtain its trajectory. The Runge-Kutta method is the preferred numerical solution method for solving these equations.

[0117] This step integrates physical modeling and numerical simulation, considering the influence of multiple factors such as air resistance and collision rebound, to establish the differential equation for the motion of the unstable rock. The Runge-Kutta method is used to solve for the trajectory, with a landing point prediction error ≤2%. This enables accurate prediction of motion trajectories, providing precise data support for safety protection.

[0118] (3) Graded early warning mechanism: Combining the simulation results of the overall slope instability trajectory and the prediction results of the falling trajectory of dangerous rocks, and at the same time, making a comprehensive judgment based on the threshold judgment results of the overall slope deformation characteristics and the local falling state of dangerous rocks, graded early warning information is generated to realize the overall-local coordinated trajectory-based graded early warning of the slope.

[0119] Level 1 (Emergency) Warning: If displacement acceleration If a dangerous rock is determined to fall immediately and its impact point is within the construction area, the system will output the direction of instability development, the coordinates of the affected area, the impact point of the dangerous rock, and an evacuation order for personnel. The first displacement acceleration threshold is an empirical value, such as 1.0.

[0120] Level 2 (High Risk) Warning: If Or, a dangerous rock may fall immediately and land outside the construction area. Within the specified range, it outputs displacement prediction curves, rockfall trajectory maps, and enhanced monitoring commands. The preset distance can be an empirical value, such as 10m.

[0121] Level 3 (Attention) Warning: If and If a dangerous rock is identified as a potential fall, the system will output a report on the deformation characteristics of the area, monitoring data on dangerous rocks, and instructions for regular inspections.

[0122] Level 4 (Stable) Warning: If and Furthermore, all dangerous rocks were stable, and routine monitoring data were output in summary.

[0123] This step establishes a four-level early warning system based on the prediction results, realizing a graded early warning mechanism. Each level corresponds to different judgment conditions and output information, achieving full-process control from routine monitoring to emergency evacuation, and improving the practicality and pertinence of early warning information.

[0124] It should be understood that the numbers S1 to S5 are only used to distinguish and facilitate the expression of different steps, and do not necessarily constitute a restriction on the execution order between the steps.

[0125] Take a certain slope (slope height 200) 500 in length Taking (e.g.,) the above method is implemented, and some of the processes and data are as follows:

[0126] Radar Deployment: Three Ku-band synthetic aperture radars were deployed in the stable area outside the slope, with coordinates as follows: , , This forms a monitoring network covering the entire slope area. The radar sampling interval is set to 5 minutes, and echo signals are collected simultaneously.

[0127] Data Inversion and Feature Extraction: The slope surface displacement field is obtained through a three-dimensional displacement inversion model. The average displacement rate in the central region is calculated. displacement acceleration Deformation uniformity coefficient Three dangerous rocks were identified, one of which had a particle size of 1.5 mm. Displacement rate of dangerous rocks Rotation angle .

[0128] Collaborative Prediction: ARIMA Model (parameters) The displacement acceleration in the central region is predicted to rise to [a certain value] in the next 24 hours. CNN model judgment 1.5 The unstable rock is considered a "potential fall". The correlation matrix calculation yields M (middle, 1.5). The value of (dangerous rock) is 0.82, indicating a strong coupling relationship.

[0129] Trajectory Prediction and Early Warning: Overall Instability Simulation Shows Sliding Direction as Coordinates of the covered area The predicted landing point of the unstable rock is... Located 5 outside the construction area The system issued a level-two warning, pushed out a trajectory map, and issued instructions to strengthen monitoring.

[0130] Implementation Results: During the monitoring period, the accuracy rate of identifying dangerous rocks was 96%, and the overall instability warning was issued 24 hours in advance. The actual landslide was consistent with the prediction, verifying the effectiveness of the method provided in this embodiment.

[0131] Example 2:

[0132] This embodiment provides a slope overall-local coordinated instability prediction system based on multi-ground radar. The system is used in the above-mentioned method and includes a data acquisition layer, a data processing layer and a model analysis layer.

[0133] The data acquisition layer includes multiple ground-based radars deployed in the stable area outside the deformation zone on the front of the slope, used to construct a synchronous monitoring network covering the entire slope area, and to collect the slope surface echo signals in real time according to a preset sampling interval.

[0134] The data processing layer obtains deformation data in the line-of-sight direction of various base radars based on the echo signal of the slope surface; it fuses the deformation data in the line-of-sight direction of various base radars, and inverts the three-dimensional displacement vector of any monitoring point on the slope surface through observation equations combined with weighted least squares estimation method to obtain the three-dimensional displacement field of the entire slope.

[0135] The model analysis layer is used to extract the overall deformation characteristics and local rockfall deformation characteristics of the slope based on the three-dimensional displacement field. Based on the overall deformation characteristics and local rockfall deformation characteristics, it predicts the overall instability trend of the slope and the state of rockfall. It also quantifies the coupling relationship between the overall deformation of each area of ​​the slope and the risk of rockfall through the correlation matrix, and determines whether to activate the overall-local coordinated early warning.

[0136] In one possible implementation, the system further includes an early warning application layer, which calculates the slope sliding surface parameters and safety factor, determines whether the slope is unstable, and simulates the overall instability trajectory of the unstable slope; simulates the falling trajectory of the unstable rock by combining the rock motion equation with numerical solution methods; combines the simulation results of the overall slope instability trajectory and the predicted results of the falling rock trajectory, and makes a comprehensive judgment based on the threshold judgment results of the overall slope deformation characteristics and the local falling rock state, to generate graded early warning information, thereby realizing a coordinated trajectory-based graded early warning for the overall and local slope.

[0137] The specific implementation of the system provided in this application can be referred to the specific embodiments of the above methods, and will not be repeated here.

[0138] The above description is merely a preferred embodiment of this application and is not intended to limit this application. Various modifications and variations can be made to this application by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application should be included within the protection scope of this application.

Claims

1. A method for predicting overall-local coordinated instability of slopes based on multi-ground radar, characterized in that, Includes the following steps: S1. Deployment and data acquisition of multiple ground-based radars: Deploy at least three ground-based radars in the stable area outside the deformation zone on the front of the slope to build a synchronous monitoring network covering the entire slope area and collect the surface echo signal of the slope in real time according to the preset sampling interval. S2. Three-dimensional displacement inversion: Based on the echo signal of the slope surface, obtain the deformation data of the line of sight of the ground radar in various locations; fuse the deformation data of the line of sight of the ground radar in various locations, and invert the three-dimensional displacement vector of any monitoring point on the slope surface through the observation equation and the weighted least squares estimation method to obtain the three-dimensional displacement field of the entire slope. S3. Extraction of overall and local deformation features of slope: Based on the three-dimensional displacement field obtained in step S2, extract the overall deformation features and local deformation features of unstable rocks of the slope. S4. Overall-local coordinated instability prediction: Based on the overall deformation characteristics of the slope and the deformation characteristics of local dangerous rocks, the overall instability trend of the slope and the state of dangerous rock falling are predicted. The coupling relationship between the overall deformation of each area of ​​the slope and the risk of falling of each dangerous rock is quantified by the correlation matrix to determine whether to activate the overall-local coordinated early warning.

2. The method according to claim 1, characterized in that, In step S2, the observation equation is: ； in, For the first Line-of-sight deformation measured by Taiwan radar For the first Taiwan radar to monitoring point The unit line-of-sight vector, ; Monitoring point P is located at The true displacement components in the direction, The observed noise follows a mean of 0 and a variance of . The normal distribution; The solution formula for the weighted least squares estimation method is as follows: ； in, For the estimated monitoring points Three-dimensional displacement vector The optimal value; It is a 3×3 geometric matrix, where each row represents a radar to a monitoring point. The unit line-of-sight vector; For the observed data vector, , The weight matrix is ​​constructed from the standard deviation of the observation error estimated by the radar coherence coefficient.

3. The method according to claim 2, characterized in that, In step S2, the weight matrix Standard deviation of observation error of a single radar Through radar coherence coefficient The estimated formula is: ;in, This is the radar wavelength.

4. The method according to claim 1, characterized in that, In step S3, the overall deformation characteristics of the slope include the average displacement rate of each region of the slope. Displacement acceleration Deformation uniformity coefficient The local deformation features of the unstable rock include the coordinates of the rock's center. Displacement rate and rotation angle θ.

5. The method according to claim 4, characterized in that, In step S3, the slope is divided into three regions—upper, middle, and lower—based on slope height. The average displacement rate, displacement acceleration, and deformation uniformity coefficient of each region are calculated using the following formulas: , , ;in, The number of monitoring points in the area. For the first in the region Displacement rate at each monitoring point , The first and the The average regional displacement rate over a time interval. The dangerous rock was identified through radar image grayscale features, and its displacement rate was determined by the formula... calculate, For dangerous rocks at time intervals Internal deformation, The radar sampling interval is given by the rotation angle θ, which is calculated by matching the contours of the dangerous rocks at adjacent time points.

6. The method according to claim 1, characterized in that, In step S4, the ARIMA time series model is used to predict the overall instability trend of the slope. The model parameters are optimized using the AIC criterion, and the displacement prediction data is obtained. If the predicted displacement acceleration value... and This triggered an overall instability warning; among which The second displacement acceleration threshold, The threshold value for the uniformity coefficient of regional deformation; A CNN classification model is constructed to predict the falling state of dangerous rocks. The model takes the displacement rate, rotation angle and overall acceleration of the region as input features and outputs the judgment results of three types of falling states: stable, potential falling and imminent falling. The correlation matrix M is an m×n two-dimensional matrix, where m is the number of slope area divisions and n is the number of identified dangerous rocks. The matrix element M(i,j) is calculated using the following formula: ;in, The covariance between the displacement acceleration of region i and the displacement rate of the j-th unstable rock. Let be the standard deviation of the displacement acceleration in the i-th region. Let be the standard deviation of the displacement rate of the j-th unstable rock; if It is determined that there is a strong coupling relationship between the overall deformation of the i-th region and the risk of the j-th dangerous rock falling, and an overall-local coordinated early warning is initiated.

7. The method according to any one of claims 1 to 6, characterized in that, The method also includes: S5, instability trajectory prediction and graded early warning: calculate the slope sliding surface parameters and safety factor, determine whether the slope is unstable and simulate the overall instability trajectory of the unstable slope; simulate the falling trajectory of the unstable rock by combining the rock motion equation with numerical solution method; combine the overall slope instability trajectory simulation results and the falling rock trajectory prediction results, and make a comprehensive judgment based on the threshold judgment results of the overall slope deformation characteristics and the local falling rock state to generate graded early warning information, so as to realize the overall-local coordinated trajectory-based graded early warning of the slope.

8. The method according to claim 7, characterized in that, In step S5, the sliding surface parameters include cohesion. internal friction angle Normal stress and shear stress Safety factor of sliding surface The calculation formula is: ; Safety factor of sliding surface With preset threshold In comparison, if To determine slope instability, the overall instability trajectory of the slope is simulated using the limit equilibrium theory in conjunction with a three-dimensional terrain model. The motion equation of the unstable rock comprehensively considers gravity, air resistance, slope support force and collision effect. The Runge-Kutta method is used to numerically solve the motion equation of the unstable rock to obtain the trajectory of the unstable rock falling.

9. The method according to claim 8, characterized in that, In step S5, the graded early warning information is a four-level graded early warning, and the specific judgment and output rules are as follows: Level 1 warning: If the displacement acceleration in the overall deformation characteristics of the slope If a dangerous rock is determined to fall immediately and the landing point is located within the construction area, output the direction of instability development, the coordinates of the covered area, the landing point of the dangerous rock, and personnel evacuation instructions. Level 2 warning: If If a dangerous rock is determined to fall immediately and the landing point is within a preset distance outside the construction area, output the displacement prediction curve, the trajectory diagram of the dangerous rock, and the instruction to strengthen monitoring. Level 3 warning: If the deformation uniformity coefficient in the overall deformation characteristics of the slope is... and When a dangerous rock is determined to be a potential falling rock, output a report on the deformation characteristics of the area, monitoring data of the dangerous rock, and instructions for regular inspections. Level 4 Warning: If and When all dangerous rocks are determined to be stable, a summary of routine monitoring data is output; among them, The first displacement acceleration threshold, The second displacement acceleration threshold, This is the threshold value for the uniformity coefficient of regional deformation.

10. A slope overall-local cooperative instability prediction system based on multi-ground radar, characterized in that, The system is used to perform the method as described in any one of claims 1 to 9, and includes a data acquisition layer, a data processing layer, and a model analysis layer; The data acquisition layer includes multiple ground-based radars deployed in the stable area outside the deformation zone on the front of the slope, used to construct a synchronous monitoring network covering the entire slope area, and to collect the slope surface echo signals in real time according to a preset sampling interval. The data processing layer obtains deformation data in the line-of-sight direction of various base radars based on the echo signal of the slope surface; it fuses the deformation data in the line-of-sight direction of various base radars, and inverts the three-dimensional displacement vector of any monitoring point on the slope surface through observation equations combined with weighted least squares estimation method to obtain the three-dimensional displacement field of the entire slope. The model analysis layer is used to extract the overall deformation characteristics and local rockfall deformation characteristics of the slope based on the three-dimensional displacement field. Based on the overall deformation characteristics and local rockfall deformation characteristics, it predicts the overall instability trend of the slope and the state of rockfall. It also quantifies the coupling relationship between the overall deformation of each area of ​​the slope and the risk of rockfall through the correlation matrix, and determines whether to activate the overall-local coordinated early warning.

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