A BeiDou-based method for early warning of highway slope disasters

Abstract

The application discloses a road slope disaster early warning method based on Beidou, and relates to the technical field of road slopes. The method comprises the following steps: determining and arranging Beidou receiving nodes in key sub-regions of a road slope to collect data and obtain road slope node data; performing displacement difference calculation on three-dimensional coordinates of the road slope node data to divide the key sub-regions into categories; extracting features of the road slope node data to obtain road slope node feature vectors, and constructing a road slope node similarity matrix; based on the road slope node similarity matrix, high-consistency trajectory clusters are obtained through a density clustering method and a contour coefficient; the road slope node feature vectors of the high-consistency trajectory clusters in the key sub-region categories are respectively reduced in dimension by using a principal component analysis method, and trajectory trends are fitted to obtain evolution indexes; the Euclidean distance is calculated by comparing the evolution indexes with indexes of a historical landslide event trajectory library to generate a risk value; and when the risk value exceeds a threshold value, an early warning is given and a risk level is established.

Description

Technical Field

[0001] This invention relates to the field of highway slope technology, specifically a method for early warning of highway slope disasters based on the BeiDou Navigation Satellite System. Background Technology

[0002] Highway slope hazards are a major geological risk source threatening traffic safety, especially in mountainous highway networks where frequent landslides and collapses often lead to road damage, traffic disruptions, and loss of life and property. With the gradual maturation of the high-precision positioning capabilities of the BeiDou Navigation Satellite System, its application in geological hazard monitoring is becoming increasingly widespread. Traditional slope monitoring methods (such as manual inspection and GNSS single-point positioning) are limited by efficiency, accuracy, and real-time performance, making it difficult to meet the needs of networked, large-scale disaster early warning systems. BeiDou-based slope monitoring technology, by acquiring real-time soil and rock displacement data, provides a new technical approach for early disaster identification and has become a key development direction for the safety and prevention of intelligent transportation infrastructure.

[0003] However, existing slope monitoring methods based on BeiDou mainly rely on threshold judgment of single-point displacement data (if the cumulative displacement of a monitoring point exceeds the threshold, it is judged that there is a risk to the highway slope), lacking deformation correlation analysis of local areas of the highway slope. As a result, it is impossible to effectively distinguish whether it is local settlement of a single monitoring point of the highway slope or slow overall coordinated deformation of multiple monitoring points, leading to a high false alarm rate and insufficient reliability of early warning. Summary of the Invention

[0004] To address the shortcomings of existing technologies, this invention provides a BeiDou-based method for early warning of highway slope disasters, thereby resolving the problems existing in the background technology.

[0005] To achieve the above objectives, the present invention provides the following technical solution: a method for early warning of highway slope disasters based on BeiDou navigation satellite system, comprising the following steps:

[0006] Step S1: By analyzing the slope, slope length, and landform of the highway slope, key sub-regions of the highway slope are determined, and several high-precision BeiDou receiving nodes are deployed in the key sub-regions of the highway slope; data is collected from the key sub-regions of the highway slope through the BeiDou receiving nodes to obtain highway slope node data.

[0007] Step S2: By performing displacement difference calculation on the three-dimensional coordinates of the highway slope node data, the displacement change trend of the nodes is obtained; by performing statistical analysis on the displacement change trend of the nodes, the key sub-region categories of the highway slope are divided, including: continuous deformation region, intermittent pulse disturbance region and static stable region; by performing feature extraction on the highway slope node data, the feature vector of the highway slope nodes is obtained.

[0008] Step S3: Construct a highway slope node similarity matrix by calculating the similarity between the feature vectors of highway slope nodes in each key sub-region category; based on the highway slope node similarity matrix, cluster the feature vectors of highway slope nodes using density clustering to obtain highway slope node trajectory clusters;

[0009] Step S4: Calculate the profile coefficient of the highway slope node trajectory cluster to obtain the cluster consistency index; use the cluster consistency index to screen the highway slope node trajectory clusters to obtain highly consistent trajectory clusters.

[0010] Step S5: Dimensionality reduction of the feature vectors of highway slope nodes in the high consistency trajectory cluster is performed by principal component analysis to obtain dimensionality reduction data of highway slope nodes; based on the key sub-region type of highway slope, the corresponding trajectory trend is fitted to the dimensionality reduction data of highway slope nodes to obtain the corresponding key sub-region curve evolution index.

[0011] Step S6: Collect evolution indicators from the historical landslide event trajectory database. By calculating the Euclidean distance between the evolution indicators of the key sub-region curve and the evolution indicators of the historical landslide event trajectory database, obtain the risk value of the highway slope sub-region. Compare the risk value of the key sub-region of the highway slope with the preset risk threshold and establish a risk warning level to achieve disaster warning for the highway slope.

[0012] Preferably, the step of obtaining the node displacement change trend by performing displacement difference calculation on the three-dimensional coordinates in the highway slope node data includes the following specific steps:

[0013] The displacement change is obtained by performing displacement difference calculation on the three-dimensional coordinates:

[0014]

[0015] in, Let represent the displacement change of the i-th high-precision BeiDou receiving node during period t. This represents the change in longitude of the i-th high-precision BeiDou receiving node during period t. = - , This represents the latitude change of the i-th high-precision BeiDou receiving node during period t. = - , This represents the change in elevation coordinates of the i-th high-precision BeiDou receiving node during period t. = - ;

[0016] The trend slope of the differential sequence of the i-th high-precision BeiDou receiving node. :

[0017]

[0018] in, The mean of the time series. Let be the mean of the differential sequence of the i-th high-precision BeiDou receiving node. = , = t is the period t, and T is the total detection period;

[0019] The dynamic threshold is calculated using the sliding window method, where w is the length of the sliding window:

[0020]

[0021] in, This represents the dynamic threshold of the i-th high-precision BeiDou receiving node within period t, used for detecting pulse points. For threshold coefficient, and Sliding windows The mean and standard deviation of the displacement changes;

[0022] The dynamic threshold of the i-th high-precision BeiDou receiving node at period t is used to calculate the pulse count:

[0023]

[0024] in, Let be the total number of pulse points of the i-th high-precision BeiDou receiving node. I() represents the dynamic threshold of the i-th high-precision Beidou receiving node in period t, I() is an indicator function, which takes the value 1 when the condition is met and 0 otherwise, and T is the total monitoring period.

[0025] Calculate stability characteristics:

[0026]

[0027] in, Let be the overall standard deviation of the displacement sequence of the i-th high-precision BeiDou receiving node, t be the period t, and T be the total detection period. Let represent the displacement change of the i-th high-precision BeiDou receiving node during period t. Let be the mean of the differential sequence of the i-th high-precision BeiDou receiving node.

[0028] Preferably, the step of statistically analyzing the displacement change trend of the nodes to classify the key sub-regions of the highway slope includes the following steps:

[0029] If the continuous deformation characteristics are satisfied simultaneously: and ,in, Let be the trend slope of the differential sequence of the i-th high-precision BeiDou receiving node. The trend slope threshold. Let be the total number of pulse points of the i-th high-precision BeiDou receiving node. This is the threshold for the proportion of pulse points;

[0030] If the characteristics of intermittent pulse impact are simultaneously satisfied: and If so, the high-precision BeiDou receiving node exhibits intermittent pulse impact characteristics;

[0031] If the static stability characteristics are satisfied simultaneously: and and , Let be the overall standard deviation of the displacement sequence of the i-th high-precision BeiDou receiving node. If the threshold value is set, then the high-precision BeiDou receiving node exhibits static stability characteristics.

[0032] By statistically analyzing the proportion of characteristic types of each high-precision BeiDou receiving node in the key sub-region of highway slope, when the proportion of a certain type of node is the highest and exceeds the preset proportion threshold, the sub-region is classified into the corresponding category. Finally, the regional categories of the key sub-region of highway slope are divided into: continuous deformation region, intermittent pulse disturbance region, and static stable region.

[0033] Preferably, the step of extracting features from the highway slope node data to obtain highway slope node feature vectors includes the following steps:

[0034] By extracting features from the highway slope node data, the displacement velocity, displacement direction angle, and node-coordinated change characteristics for each cycle are obtained:

[0035]

[0036] in, Let be the displacement velocity of the i-th high-precision BeiDou receiving node in period t. Let represent the displacement change of the i-th high-precision BeiDou receiving node during period t. For periodic intervals;

[0037]

[0038] in, Let be the displacement direction angle of the i-th high-precision BeiDou receiving node in period t. This represents the latitude change of the i-th high-precision BeiDou receiving node during period t. This represents the change in longitude of the i-th high-precision BeiDou receiving node during period t;

[0039] Characteristics of node collaborative change:

[0040]

[0041] in, This represents the displacement similarity between the i-th and j-th high-precision BeiDou receiving nodes. Let represent the displacement change of the i-th high-precision BeiDou receiving node during period t. Let be the displacement change of the j-th high-precision BeiDou receiving node during period t;

[0042]

[0043] in, This represents the cooperative change characteristics of neighboring nodes of the i-th high-precision BeiDou receiving node in period t. This represents the displacement similarity between the i-th and j-th high-precision BeiDou receiving nodes. As the displacement similarity threshold, This represents the cooperative change characteristics of neighboring nodes of the i-th high-precision BeiDou receiving node in period t. This represents the number of neighboring nodes. This is an indicator function; it returns 1 if the condition is met, and 0 otherwise.

[0044] For the i-th high-precision BeiDou receiving node, the feature vector of the highway slope node is [ (t), , ].

[0045] Preferably, the step of constructing a highway slope node similarity matrix by calculating the similarity between feature vectors of highway slope nodes in each key sub-region category includes the following steps:

[0046] Calculate the similarity between feature vectors of highway slope nodes in each key sub-region category, and construct a highway slope node similarity matrix:

[0047]

[0048] in, Let be the similarity between the feature vectors of the i-th and j-th highway slope nodes in the highway slope node similarity matrix, where t is the period t and T is the total detection period. For displacement-velocity similarity, For the similarity of displacement direction angles, Similarity of node collaborative change features , and These are the weights for displacement velocity similarity, displacement direction angle similarity, and node cooperative change feature similarity, respectively.

[0049] Preferably, the step of obtaining the cluster consistency index by calculating the profile coefficient of the highway slope node trajectory cluster includes the following steps:

[0050] By calculating the profile coefficient of the trajectory cluster of highway slope nodes, the cluster consistency index is obtained:

[0051]

[0052] in, Let be the cluster consistency index of the trajectory cluster of the c-th highway slope node. Let be the number of feature vectors of highway slope nodes in the trajectory cluster of the c-th highway slope node. is the silhouette coefficient of the feature vector of the i-th highway slope node.

[0053] Preferably, the step of reducing the dimensionality of the feature vectors of highway slope nodes in the highly consistent trajectory cluster using principal component analysis to obtain dimensionality-reduced highway slope node data includes the following specific steps:

[0054] Principal component analysis was used to reduce the dimensionality of the feature vectors of highway slope nodes in the highly consistent trajectory cluster, resulting in dimensionality-reduced highway slope node data.

[0055]

[0056] in, This represents the dimensionality reduction data of the highway slope node of the i-th high-precision BeiDou receiving node in a highly consistent cluster under period t. This represents a one-dimensional dimensionality reduction function for principal component analysis. This represents the feature vector of the highway slope node of the i-th high-precision Beidou receiving node in a high-consistency cluster under period t.

[0057] The dimensionality reduction data of highway slope nodes in highly consistent clusters are as follows: , =[ , ,..., ].

[0058] Preferably, for the key sub-region type of the highway slope, the corresponding trajectory trend fitting is performed on the dimensionality reduction data of the highway slope nodes to obtain the corresponding key sub-region curve evolution index, including the following specific steps:

[0059] For the region of continuous deformation, an exponential function is fitted using the least squares method:

[0060]

[0061] in, For the region of continuous deformation, it is an exponential function. , , Here are the parameters of the exponential function, and t is the period t.

[0062] For the intermittent pulse disturbance region, a sinusoidal trigonometric function is fitted using a fast Fourier transform:

[0063]

[0064] in, For the region of intermittent pulse disturbance, the sinusoidal trigonometric function is... Let m be the amplitude of the m-th sine wave. Let be the angular frequency of the m-th sine wave. Let be the phase angle of the m-th sine wave. This is the constant term of the sine trigonometric function;

[0065] Residual analysis was performed on the statically stable region, and a horizontal straight line was fitted.

[0066]

[0067] in, A horizontal straight line representing the statically stable region. The constant corresponding to the horizontal line;

[0068] The evolution index of the key sub-region curve corresponding to the key sub-region category, =[ , ], =[ , ], = ,in, For indicators of regions of continuous deformation, This is an indicator for the region of intermittent pulse disturbances. This is an indicator for the statically stable region.

[0069] Preferably, the step of obtaining the risk value of the highway slope sub-region by calculating the Euclidean distance between the evolution index of the key sub-region curve and the evolution index of the historical landslide event trajectory database includes the following specific steps:

[0070] The risk value of the highway slope sub-region is obtained by calculating the Euclidean distance between the evolution index of the key sub-region curve and the evolution index of the historical landslide event trajectory database.

[0071]

[0072] Wherein, FX represents the risk value of the highway slope sub-area. YZ represents the l-th index in the highway slope curve evolution index, YZ=[ , , YZ is the evolution index of highway slope curve. Let L be the l-th indicator in the evolution index of the historical landslide event trajectory database, where L is the total number of indicators and l is the index of the l-th indicator.

[0073] Preferably, the risk value of the key sub-region of the highway slope is compared with a preset risk threshold to establish a risk warning level, including the following specific steps:

[0074] If the risk value of a key sub-area of ​​a highway slope exceeds the preset risk threshold, an early warning will be issued and a risk level will be established: Level I (Severe): FX ≥ 0.8 × preset risk threshold. Traffic on the corresponding road section will be closed immediately, a warning line will be set up, emergency reinforcement of the slope will be initiated, and personnel within a 1-kilometer radius will be evacuated.

[0075] Level II (Severe): 0.6 × preset risk threshold ≤ FX < 0.8 × preset risk threshold, implement traffic control, complete the surface anchoring treatment of the slope waist within 24 hours, and increase the monitoring frequency to once per hour;

[0076] Level III (General): 0.4 × preset risk threshold ≤ FX < 0.6 × preset risk threshold. Issue road condition warnings, guide vehicles to detour, conduct manual geological inspections, investigate crack development, and adjust the monitoring frequency to once every 4 hours.

[0077] Level IV Warning: If FX < 0.4 × preset risk threshold, the sensor should be included in the key monitoring list, abnormal data should be recorded, and technical personnel should be dispatched to verify the sensor status on-site.

[0078] Beneficial effects

[0079] This invention provides a method for early warning of highway slope disasters based on BeiDou navigation satellite system. It has the following beneficial effects:

[0080] (1) Construct a node similarity matrix and use density clustering to generate a cluster of highway slope node trajectories. Quantify the association strength of the node group in the similarity matrix by calculating the dynamic similarity of displacement velocity, direction angle and collaborative features between nodes. Density clustering adaptively identifies node groups with similar displacement patterns, while filtering out isolated noise points caused by equipment failure or local rock block fallout.

[0081] (2) Screening high-consistency trajectory clusters based on profile coefficients significantly improves the reliability of early warning targets. The profile coefficient calculation determines the overall consistency of node characteristics within the cluster (such as the concentration of displacement direction and velocity synchronization), retaining only clusters that meet the index criteria. These high-consistency clusters represent dangerous areas with strong deformation synergy and clear evolution trends within the slope (such as the toe shear failure zone), eliminating interference signals caused by temporary construction vibrations or local collapses. The screening mechanism significantly reduces the data scale of subsequent analysis, allowing computational resources to focus on the core areas that truly threaten slope stability.

[0082] (3) A data-driven hierarchical early warning mechanism was established by calculating risk values ​​using Euclidean distance matching evolution indicators. This method compares the current slope evolution characteristics (such as the exponential growth slope of persistent areas and the vibration dominant frequency of pulse areas) with indicators from a historical landslide event database, and uses a distance mapping function to convert them into risk probability values ​​in the 0-1 interval. Based on the risk values, a four-level response is dynamically triggered: from Level I (closed road sections, evacuation of personnel) to Level IV (routine monitoring). This pattern matching mechanism replaces the traditional subjective threshold judgment, reducing the false alarm rate of the project. Attached Figure Description

[0083] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0084] Figure 1 This is a flowchart illustrating the steps of a BeiDou-based early warning method for highway slope disasters proposed in this invention.

[0085] Figure 2 This is a step-by-step diagram of a BeiDou-based early warning method for highway slope disasters proposed in this invention. Detailed Implementation

[0086] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0087] Please see Figure 1-2 The present invention provides a technical solution: a method for early warning of highway slope disasters based on Beidou.

[0088] Step S1: By analyzing the slope, slope length, and landform of the highway slope, key sub-regions of the highway slope are determined, and several high-precision BeiDou receiving nodes are deployed in the key sub-regions of the highway slope; data is collected from the key sub-regions of the highway slope through the BeiDou receiving nodes to obtain highway slope node data.

[0089] By analyzing the slope, length, and topography of the highway slope, key sub-regions of the highway slope were identified, and several high-precision BeiDou receiving nodes were deployed in these key sub-regions. In addition to the BeiDou module, each BeiDou receiving node also integrates an inertial measurement unit and a three-axis inclinometer.

[0090] It should be noted that by analyzing the slope, length, and landform of the highway slope, key sub-regions of the highway slope are identified. For example: Slope: Through digital elevation models or field surveys, the slope is divided into gentle slope areas (<15°), medium slope areas (15°~30°), and steep slope areas (>30°). High and steep slope sections with a slope greater than 30° and slope abrupt change zones (such as slope shoulder turning points) are listed as key sub-areas of highway slopes, as these areas are prone to stress concentration and shallow slip risks; Slope length: For ultra-long slope sections with a longitudinal continuous length greater than 50 meters, they are listed as key sub-areas of highway slopes, and the density of monitoring points should be increased by 30% for every additional 20 meters to ensure that deformation gradients can be effectively captured; Geomorphology: Due to the curvature characteristics of convex slopes, which are gentle at the top and steep at the bottom, the focus should be on the shear zone at the toe of the slope (such as the base of retaining walls); For concave slopes, which are steep at the top and gentle at the bottom, the monitoring center should be placed in the tension zone at the top of the slope (the rear edge crack zone); For stepped slopes, monitoring points should be placed at the edges of each level of platform to prevent local collapse.

[0091] It should be noted that the BeiDou receiving node includes a BeiDou module, an inertial measurement unit (IMU), and a triaxial inclinometer. The BeiDou module provides millimeter-level positioning accuracy for monitoring the node's three-dimensional displacement; the IMU and triaxial inclinometer sense the node's attitude changes, assisting in determining the deformation direction and angle of the slope; and temperature and humidity sensors monitor the impact of environmental factors on slope stability. The IMU includes acceleration (linear acceleration along the X, Y, and Z axes, unit: m / s²), used to calculate the node's motion trend (e.g., acceleration, deceleration); angular velocity (rotational angular velocity around the X, Y, and Z axes, unit: rad / s), reflecting the node's attitude changes (e.g., tilting, torsion); and motion trajectory (generating the node's three-dimensional motion trajectory through the integration of acceleration and angular velocity, assisting in determining the displacement mode of the slope's soil and rock mass (e.g., sliding, overturning). The triaxial inclinometer measures tilt angle (tilt angle along the X, Y, and Z axes), reflecting the slope's inclination state at the node's location. Rate of change of angle: the amount of change in tilt angle per unit time, used to identify sudden tilting (such as rapid changes in tilt angle before a landslide).

[0092] Data is collected from key sub-regions of the highway slope through the Beidou receiving node to obtain highway slope node data. The highway slope node data includes three-dimensional coordinates, acceleration, angular velocity, tilt angle, and rate of change of angular velocity.

[0093] Step S2: By performing displacement difference calculation on the three-dimensional coordinates of the highway slope node data, the displacement change trend of the nodes is obtained; by performing statistical analysis on the displacement change trend of the nodes, the key sub-region categories of the highway slope are divided, including: continuous deformation region, intermittent pulse disturbance region and static stable region; by performing feature extraction on the highway slope node data, the feature vector of the highway slope nodes is obtained.

[0094] The three-dimensional coordinate time series of highway slope node data in each key sub-region of the highway slope is as follows: =( , , ), where t is the period t, , , The longitude, latitude, and elevation coordinates of the i-th high-precision BeiDou receiving node in period t are respectively.

[0095] The displacement change is obtained by performing displacement difference calculation on the three-dimensional coordinates:

[0096]

[0097] in, Let represent the displacement change of the i-th high-precision BeiDou receiving node during period t. This represents the change in longitude of the i-th high-precision BeiDou receiving node during period t. = - , This represents the latitude change of the i-th high-precision BeiDou receiving node during period t. = - , This represents the change in elevation coordinates of the i-th high-precision BeiDou receiving node during period t. = - .

[0098] = : The displacement sequence of the i-th high-precision Beidou receiving node, where T is the total detection period.

[0099] Displacement sequence of the i-th high-precision BeiDou receiving node The displacement time series was fitted using linear regression:

[0100]

[0101] in, Let represent the displacement change of the i-th high-precision BeiDou receiving node during period t. Let be the trend slope of the differential sequence of the i-th high-precision BeiDou receiving node, and t be the period t. Let represent the linear regression intercept term of the displacement sequence of the i-th high-precision BeiDou receiving node. This represents the regression residual of the i-th high-precision BeiDou receiving node in period t.

[0102] The trend slope of the differential sequence of the i-th high-precision BeiDou receiving node. :

[0103]

[0104] in, The mean of the time series. Let be the mean of the differential sequence of the i-th high-precision BeiDou receiving node. = , = t is the period t, and T is the total detection period.

[0105] The dynamic threshold is calculated using the sliding window method, where w is the length of the sliding window:

[0106]

[0107] in, This represents the dynamic threshold of the i-th high-precision BeiDou receiving node within period t, used for detecting pulse points. For threshold coefficient, and Sliding windows The mean and standard deviation of the displacement changes within the range.

[0108] It should be noted that, and Sliding windows The mean and standard deviation of the displacement within the range, , = .

[0109] It should be noted that the threshold coefficient can be customized, for example: =3, corresponding to "3" "in principle.

[0110] The dynamic threshold of the i-th high-precision BeiDou receiving node at period t is used to calculate the pulse count:

[0111]

[0112] in, Let be the total number of pulse points of the i-th high-precision BeiDou receiving node. I() represents the dynamic threshold of the i-th high-precision BeiDou receiving node in period t, I() is an indicator function that takes the value 1 when the condition is met and 0 otherwise, and T is the total monitoring period.

[0113] Calculate stability characteristics:

[0114]

[0115] in, Let be the overall standard deviation of the displacement sequence of the i-th high-precision BeiDou receiving node, t be the period t, and T be the total detection period. Let represent the displacement change of the i-th high-precision BeiDou receiving node during period t. Let be the mean of the differential sequence of the i-th high-precision BeiDou receiving node.

[0116] Each high-precision BeiDou receiving node is classified into feature types, including: continuous deformation features, intermittent pulse impact features, and static stability features.

[0117] It should be noted that the continuous deformation characteristic must simultaneously satisfy: and ,in, Let be the trend slope of the differential sequence of the i-th high-precision BeiDou receiving node. The trend slope threshold. Let be the total number of pulse points of the i-th high-precision BeiDou receiving node. If the threshold value is the percentage of pulse points, then the high-precision BeiDou receiving node exhibits continuous deformation characteristics.

[0118] It should be noted that the characteristics of intermittent pulse impact are as follows: and If so, the high-precision BeiDou receiving node has intermittent pulse impact characteristics.

[0119] It should be noted that static stability characteristics are defined if the following conditions are met simultaneously: and and , Let be the overall standard deviation of the displacement sequence of the i-th high-precision BeiDou receiving node. If the threshold value is used, then the high-precision BeiDou receiving node has static stability characteristics.

[0120] By statistically analyzing the displacement change trends of the nodes, the key sub-region categories of the corresponding key sub-regions of the highway slope are obtained.

[0121] It should be noted that statistical analysis of the displacement change trends of the nodes revealed that the key sub-region of the highway slope contains several high-precision BeiDou receiving nodes. By statistically analyzing the proportion of characteristic types of each high-precision BeiDou receiving node within the key sub-region of the highway slope, when the proportion of a certain type of node is the highest and exceeds a preset threshold (e.g., 60%), the sub-region is classified into the corresponding category. Ultimately, the key sub-regions of the highway slope are categorized as follows: continuous deformation region, intermittent pulse disturbance region, and statically stable region.

[0122] It should be noted that the continuous deformation region: displacement trend slope Significant (continuous growth or decay) and low proportion of pulse points (no sudden drastic deformation) indicate that the nodal displacement exhibits continuous and regular changes, such as the continuous sliding of surface soil and rock under the action of external forces such as gravity and rainwater on the slope; Intermittent pulse disturbance area: high proportion of pulse points, but no significant trend slope, and the displacement shows periodic sudden disturbances. For example, local soil and rock inside the slope undergoes intermittent deformation due to stress concentration and release, or is affected by instantaneous loads such as earthquakes and construction; Static stable area: low trend slope and low proportion of pulse points, and small overall standard deviation of displacement sequence, the overall displacement tends to be stable, but there may be extremely slow potential deformation (such as long-term creep).

[0123] By extracting features from the highway slope node data, the displacement velocity, displacement direction angle, and node-coordinated change characteristics for each cycle are obtained:

[0124]

[0125] in, Let be the displacement velocity of the i-th high-precision BeiDou receiving node in period t. Let represent the displacement change of the i-th high-precision BeiDou receiving node during period t. The periodic interval is used.

[0126]

[0127] in, Let be the displacement direction angle of the i-th high-precision BeiDou receiving node in period t. This represents the latitude change of the i-th high-precision BeiDou receiving node during period t. This represents the change in longitude of the i-th high-precision BeiDou receiving node during period t.

[0128] Characteristics of node collaborative change:

[0129]

[0130] in, This represents the displacement similarity between the i-th and j-th high-precision BeiDou receiving nodes. Let represent the displacement change of the i-th high-precision BeiDou receiving node during period t. Let be the displacement change of the j-th high-precision BeiDou receiving node during period t.

[0131]

[0132] in, This represents the cooperative change characteristics of neighboring nodes of the i-th high-precision BeiDou receiving node in period t. This represents the displacement similarity between the i-th and j-th high-precision BeiDou receiving nodes. As the displacement similarity threshold, This represents the cooperative change characteristics of neighboring nodes of the i-th high-precision BeiDou receiving node in period t. This represents the number of neighboring nodes. This is an indicator function; it is 1 if the condition is met, and 0 otherwise.

[0133] It should be noted that the term "nearby node" refers to other monitoring nodes that are physically adjacent to the i-th high-precision BeiDou receiving node. For example, a high-precision BeiDou receiving node whose horizontal or three-dimensional spatial distance from the i-th high-precision BeiDou receiving node is less than a certain value (such as 5 meters or 10 meters) is considered a nearby node of the i-th high-precision BeiDou receiving node.

[0134] For the i-th high-precision BeiDou receiving node, the feature vector of the highway slope node is [ (t), , ].

[0135] Step S3: Construct a highway slope node similarity matrix by calculating the similarity between the feature vectors of highway slope nodes in each key sub-region category; based on the highway slope node similarity matrix, cluster the feature vectors of highway slope nodes using density clustering to obtain highway slope node trajectory clusters.

[0136] For each detection period t, the feature vector of the highway slope node is [ (t), , The data is standardized and mapped to the range [0,1].

[0137] Calculate the similarity between feature vectors of highway slope nodes in each key sub-region category, and construct a highway slope node similarity matrix:

[0138]

[0139] in, Let be the similarity between the feature vectors of the i-th and j-th highway slope nodes in the highway slope node similarity matrix, where t is the period t and T is the total detection period. For displacement-velocity similarity, For the similarity of displacement direction angles, Similarity of node collaborative change features , and These are the weights for displacement velocity similarity, displacement direction angle similarity, and node cooperative change feature similarity, respectively.

[0140] It should be noted that the displacement velocity similarity = , Let be the displacement velocity of the i-th high-precision BeiDou receiving node in period t. Let be the displacement velocity and displacement direction angle similarity of the j-th high-precision BeiDou receiving node in period t. =cos(| - |), Let be the displacement direction angle of the i-th high-precision BeiDou receiving node in period t. Let be the displacement direction angle of the j-th high-precision BeiDou receiving node in period t. =1-| - |, This represents the cooperative change characteristics of neighboring nodes of the i-th high-precision BeiDou receiving node in period t. The characteristics of the coordinated change of neighboring nodes of the j-th high-precision BeiDou receiving node in period t.

[0141] It should be noted that, , and These are the weights for displacement velocity similarity, displacement direction angle similarity, and nodal cooperative change feature similarity, respectively, which can be taken as... =0.5, =0.3, =0.2, displacement velocity, as the core indicator, directly quantifies the dynamic intensity of slope deformation. Its numerical change is strongly correlated with the landslide hazard development process. For example, a continuous increase in velocity often indicates instability risk, so it is given the highest weight to highlight the characterization of the immediate deformation state. Displacement direction angle reflects the spatial orientation of deformation and can help determine the sliding trend (such as whether it is along the main sliding surface). Although it is not as directly related to the hazard threshold as velocity, it can provide spatial constraints for deformation pattern recognition, especially in multi-node collaborative analysis, where it can calibrate deformation consistency. Node collaborative change characteristics, as a group correlation indicator, are used to characterize the overall deformation coordination of the slope rock mass. A sudden change in a single node may be caused by local disturbance, while multi-node collaborative anomalies are more likely to reflect regional stability deterioration. However, its role depends on the basic data of velocity and direction angle, so it is used as an auxiliary weight to correct the reliability of the overall assessment. This allocation follows the slope monitoring priority of "dynamic intensity > spatial direction > group correlation" and ensures the dominant role of core deformation characteristics in risk assessment through weight gradient, while also taking into account the need for the integration of multi-dimensional information.

[0142] Based on the highway slope node similarity matrix, the feature vectors of the highway slope nodes are clustered using density clustering to obtain highway slope node trajectory clusters. First, the highway slope node similarity matrix is ​​converted into a highway slope node similarity distance matrix: , This represents the similarity distance between the eigenvectors of the i-th and j-th highway slope nodes in the distance matrix. Then, based on the similarity distance matrix, a K-distance graph is constructed (for the i-th highway slope node, calculate its distances to all other highway slope nodes, sort them in ascending order, and take the K-th minimum distance value). (K) Sort all the Kth minimum distance values ​​of the highway slope nodes in descending order and plot a line graph (horizontal axis is the node number, vertical axis is the Kth minimum distance value corresponding to the node number). Select the vertical coordinate value corresponding to the inflection point in the K-distance graph (the inflection point can be determined by visualizing the K-distance graph) as the neighborhood radius of the density clustering method, and initialize the minimum number of samples for the density clustering method. Use the neighborhood radius of the density clustering method as the criterion for determining the neighborhood. For example, if the similarity distance between the feature vector of the i-th highway slope node and the feature vector of the j-th highway slope node is less than the neighborhood radius, then the feature vector of the j-th highway slope node is considered to be in the neighborhood of the feature vector of the i-th highway slope node. Then, core points, boundary points, and noise points are identified based on the number of points in their neighborhoods: if a node's neighborhood contains no fewer than the set minimum sample size, the node is identified as a core point, which is a key node for clustering; boundary points are nodes whose neighborhood contains fewer than the minimum sample size but are within the neighborhood of a core point; and nodes that are neither core points nor boundary points are noise points, as these nodes have weak correlations with other nodes. Finally, adjacent core point clusters are merged, that is, clusters formed by core points that are density-connected to each other are integrated into a complete cluster, thereby generating the final highway slope node clustering result, resulting in the highway slope node trajectory cluster.

[0143] Step S4: Calculate the profile coefficient of the highway slope node trajectory cluster to obtain the cluster consistency index; use the cluster consistency index to screen the highway slope node trajectory cluster to obtain a highly consistent trajectory cluster.

[0144] By calculating the profile coefficient of the trajectory cluster of highway slope nodes, the cluster consistency index is obtained:

[0145]

[0146] in, Let be the cluster consistency index of the trajectory cluster of the c-th highway slope node. Let be the number of feature vectors of highway slope nodes in the trajectory cluster of the c-th highway slope node. is the silhouette coefficient of the feature vector of the i-th highway slope node.

[0147] It should be noted that, Let be the silhouette coefficient of the feature vector of the i-th highway slope node. , It represents the average dissimilarity between the feature vector of the i-th highway slope node and other highway slope nodes within the same highway slope node trajectory cluster. It is the minimum average dissimilarity between the feature vector of the i-th highway slope node and other highway slope nodes within the same trajectory cluster. For example, the feature vector of the i-th highway slope node belongs to the trajectory cluster of the c-th highway slope node. If other highway slope node trajectory families are represented, then = b .

[0148] By filtering the highway slope node trajectory clusters using the cluster consistency index, highly consistent trajectory clusters are obtained. The feature vector of the highway slope node in the highly consistent cluster is then […]. ].

[0149] It should be noted that the cluster consistency index is used to screen highway slope node trajectory clusters to obtain highly consistent trajectory clusters. After calculating the consistency index of each highway slope node trajectory cluster, it is necessary to conduct a screening of strong trend consistency clusters based on this index. A screening threshold for the consistency index is set (e.g., 0.6). For each cluster, if its consistency index reaches or exceeds the threshold, it indicates that the nodes within the cluster exhibit strong trend consistency in multiple dimensions such as displacement velocity, orientation angle, and cooperative characteristics, and is thus determined to be a highly consistent trajectory cluster.

[0150] Step S5: Dimensionality reduction of the feature vectors of highway slope nodes in the high consistency trajectory cluster is performed by principal component analysis to obtain dimensionality reduction data of highway slope nodes; based on the key sub-region type of highway slope, the corresponding trajectory trend is fitted to the dimensionality reduction data of highway slope nodes to obtain the corresponding key sub-region curve evolution index.

[0151] Principal component analysis was used to reduce the dimensionality of the feature vectors of highway slope nodes in the highly consistent trajectory cluster, resulting in dimensionality-reduced highway slope node data.

[0152]

[0153] in, This represents the dimensionality reduction data of the highway slope node of the i-th high-precision BeiDou receiving node in a highly consistent cluster under period t. This represents a one-dimensional dimensionality reduction function for principal component analysis. This represents the feature vector of the highway slope node of the i-th high-precision BeiDou receiving node in a high-consistency cluster under period t.

[0154] The dimensionality reduction data of highway slope nodes in highly consistent clusters are as follows: , =[ , ,..., ].

[0155] Based on the aforementioned key sub-region types of highway slopes, trend fitting is performed on the dimensionality-reduced data of all highway slope nodes in the highly consistent trajectory clusters under each key sub-region type of highway slope.

[0156] For the region of continuous deformation, an exponential function is fitted using the least squares method:

[0157]

[0158] in, For the region of continuous deformation, it is an exponential function. , , is the parameter of the exponential function, and t is the period t.

[0159] It should be noted that, by using the least squares method to fit the exponential function, the dimensionality of the highway slope node data in the highly consistent clusters is first reduced. Perform least-squares fitting and solve for the coefficients A. If the exponential function It was determined to be a continuous acceleration trend; the goodness of fit was calculated. ,when The fit is considered valid at that time.

[0160] For the intermittent pulse disturbance region, a sinusoidal trigonometric function is fitted using a fast Fourier transform:

[0161]

[0162] in, For the region of intermittent pulse disturbance, the sinusoidal trigonometric function is... Let m be the amplitude of the m-th sine wave. Let be the angular frequency of the m-th sine wave. Let be the phase angle of the m-th sine wave. This is the constant term of the sine trigonometric function.

[0163] It should be noted that the dimensionality reduction data of highway slope nodes in highly consistent clusters... Perform a Fast Fourier Transform to extract the top three frequency components by energy percentage. , , These are the top three frequency components in terms of energy percentage.

[0164] Residual analysis was performed on the statically stable region, and a horizontal straight line was fitted.

[0165]

[0166] in, A horizontal straight line representing the statically stable region. This is the constant corresponding to the horizontal line.

[0167] It should be noted that selecting the corresponding curve fitting for each key sub-region type reveals significant differences in deformation characteristics across different regions. Targeted mathematical models are needed to capture their evolutionary patterns to improve early warning accuracy. In regions of continuous deformation, displacement exhibits continuous and regular changes (e.g., continuous slippage), with a significant trend slope and a low proportion of pulse points. Exponential functions can effectively fit this continuously accelerating or decaying deformation trend, especially when the parameter is set, as it can intuitively reflect the displacement rate increase, aligning with the characteristics of gradual instability of slope soil and rock under gravity or rainwater. In regions of intermittent pulse disturbance, displacement manifests as periodic sudden disturbances (e.g., stress concentration-release or external load influence), with a high proportion of pulse points but an insignificant trend slope. Fast Fourier transform combined with sine trigonometric function fitting can extract the frequency, amplitude, and other features of the disturbance, accurately characterizing the periodic deformation pattern. In regions of static stability, displacement generally tends to be stable, with low trend slope and a low proportion of pulse points. Horizontal straight-line fitting can be used to verify its stability through residual analysis. Even with extremely slow potential deformation, it can be monitored using a constant term benchmark value, avoiding misjudging a stable state as a precursor to disaster.

[0168] Finally, the evolution index of the key sub-region curve corresponding to the key sub-region category is obtained. =[ , ], =[ , ], = ,in, For indicators of regions of continuous deformation, This is an indicator for the region of intermittent pulse disturbances. This is an indicator for the statically stable region.

[0169] Step S6: Collect evolution indicators from the historical landslide event trajectory database. By calculating the Euclidean distance between the evolution indicators of the key sub-region curve and the evolution indicators of the historical landslide event trajectory database, obtain the risk value of the highway slope sub-region. Compare the risk value of the key sub-region of the highway slope with the preset risk threshold and establish a risk warning level to achieve disaster warning for the highway slope.

[0170] Evolutionary indices from a historical landslide event trajectory database are collected. The Euclidean distance between the evolutionary indices of the key sub-region curves and the evolutionary indices from the historical landslide event trajectory database is calculated to obtain the risk value of the highway slope sub-region.

[0171]

[0172] Wherein, FX represents the risk value of the highway slope sub-area. YZ represents the l-th index in the highway slope curve evolution index, YZ=[ , , YZ is the evolution index of highway slope curve. Let L be the l-th indicator in the evolution index of the historical landslide event trajectory database, where L is the total number of indicators and l is the index of the l-th indicator.

[0173] It should be noted that the historical landslide event trajectory database contains evolutionary indicators related to highway slope disasters. These indicators are derived from monitoring data of past landslide events obtained through BeiDou receiving nodes. , =[ , , Specifically, this includes: the exponential curve parameters in the persistent deformation area index of the historical landslide event trajectory database. , The sine function parameters in the intermittent pulse disturbance area index of the historical landslide event trajectory database reflect the continuous acceleration trend of displacement before the landslide. , The constant corresponding to the horizontal straight line in the static stability region index of the historical landslide event trajectory database: , representing the baseline state that can potentially deform slowly.

[0174] The risk values ​​of key sub-regions of the highway slope are compared with preset risk thresholds to establish risk warning levels. Based on the unique structural location of each key sub-region of the highway slope (e.g., at the top, middle, or bottom of the slope), different levels are defined, and specific response levels are set accordingly. Warning information, including risk level, location identifier, trend description, and handling suggestions, is simultaneously released to the remote management center and local front-end station via BeiDou short message service. Simultaneously, the system can activate on-site voice prompts and visual traffic lights, realizing an integrated multi-channel warning strategy of "front-end judgment + back-end push + local prompts." For example: Level I (Severe): FX ≥ 0.8 × preset risk threshold, immediately close the corresponding road section to traffic, set up a warning line, initiate emergency reinforcement work on the slope middle (e.g., grouting reinforcement, anti-slide pile construction), and organize the evacuation of personnel within a 1-kilometer radius.

[0175] Level II (Severe): 0.6 × preset risk threshold ≤ FX < 0.8 × preset risk threshold, implement traffic control (speed limit 20km / h, one-way traffic), complete the surface anchoring treatment of the slope waist within 24 hours, and increase the monitoring frequency to 1 time / hour.

[0176] Level III (General): 0.4 × preset risk threshold ≤ FX < 0.6 × preset risk threshold, issue road condition warnings, guide vehicles to detour, conduct manual geological inspections, investigate crack development, and adjust the monitoring frequency to once every 4 hours.

[0177] Level IV (Caution): FX < 0.4 × preset risk threshold, included in key monitoring targets, abnormal data recorded, technical personnel arranged to verify sensor status on-site, and regular monitoring frequency maintained (1 time / day).

[0178] This paper proposes a method for early warning of highway slope disasters based on BeiDou satellite positioning. Through multi-dimensional data fusion and intelligent analysis technology, it achieves accurate identification and graded early warning of slope instability risks. The method first deploys monitoring nodes integrating BeiDou modules, inclinometers, and environmental sensors in key areas of the slope (such as the slope top, slope surface, and slope toe) to collect high-precision displacement data. Then, it extracts displacement velocity, orientation angle, and node-coordinated change characteristics, and divides the slope into three sub-regions based on deformation patterns: continuous deformation, intermittent pulse disturbance, and static stability. Finally, through clustering and historical pattern matching, it generates quantifiable risk warning instructions for action.

[0179] This method overcomes the bottleneck of traditional single-point monitoring by constructing a node similarity matrix and using density clustering to generate trajectory clusters. It quantifies the association strength of node groups in the similarity matrix by calculating the dynamic similarity of displacement velocity, orientation angle, and collaborative features between nodes (such as the cosine of the displacement orientation angle difference and the difference in collaborative change features). Density clustering adaptively identifies node groups with similar displacement patterns (such as node clusters with continuous synchronous sliding), while filtering out isolated noise points caused by equipment failure or local rock fragment loss. This process reveals the spatial collaborative laws of slope soil and rock deformation, providing a data foundation for identifying potential unified slip zones.

[0180] Using profile coefficients to screen high-consistency trajectory clusters significantly improves the reliability of early warning targets. The profile coefficient calculation determines the overall consistency of node characteristics within a cluster (e.g., concentration of displacement direction, velocity synchronization), retaining only clusters with indices meeting certain criteria (e.g., thresholds above 0.6). These high-consistency clusters represent hazardous areas with strong deformation synergy and clear evolution trends within the slope (e.g., shear failure zones at the toe of the slope), eliminating interference signals caused by temporary construction vibrations or localized collapses. This screening mechanism significantly reduces the data size for subsequent analysis, allowing computational resources to focus on the core areas that truly threaten slope stability.

[0181] A data-driven, tiered early warning mechanism was established by calculating risk values ​​using Euclidean distance-matched evolutionary indices. This method compares current slope evolution characteristics (such as the exponential growth slope of persistent areas and the dominant vibration frequency of pulsating areas) with indices from a historical landslide event database, transforming them into risk probability values ​​in the 0-1 range using a distance mapping function. Based on these risk values, a four-level response is dynamically triggered: from Level I (road closure, personnel evacuation) to Level IV (routine monitoring), and early warning information is pushed via BeiDou short message service. This pattern matching mechanism replaces traditional subjective threshold judgments, upgrading the early warning basis from single-point displacement exceedances to multi-node collaborative evolutionary anomalies, thus reducing the false alarm rate in engineering projects.

[0182] It should be noted that, in this document, relational terms such as "first" and "second" are used merely to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, the phrase "comprising an element defined as..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0183] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A Beidou-based highway slope disaster early warning method, characterized in that: The method comprises the following steps: Step S1: determining a highway slope key sub-region by analyzing the slope, slope length and landform of the highway slope, arranging a plurality of Beidou receiving nodes in the highway slope key sub-region and collecting data to obtain highway slope node data; Step S2: performing displacement difference calculation on three-dimensional coordinates in the highway slope node data to obtain a node displacement change trend and perform statistical analysis, dividing a key sub-region category of the highway slope key sub-region, the key sub-region category comprising a persistent deformation region, an intermittent pulse disturbance region and a static stable region, and performing feature extraction on the highway slope node data to obtain a highway slope node feature vector; Step S3: calculating the similarity between highway slope node feature vectors in each key sub-region category to construct a highway slope node similarity matrix, and clustering the highway slope node feature vectors to obtain a highway slope node trajectory cluster; Step S4: calculating a contour coefficient of the highway slope node trajectory cluster to obtain a clustering cluster consistency index, and screening the highway slope node trajectory cluster according to the clustering cluster consistency index to obtain a high-consistency trajectory cluster; Step S5: performing dimension reduction on the highway slope node feature vectors in the high-consistency trajectory cluster to obtain highway slope node reduced dimension data, and performing trajectory trend fitting on the highway slope node reduced dimension data to obtain a key sub-region curve evolution index; Step S6: collecting an evolution index in a historical landslide event trajectory library, calculating the Euclidean distance between the key sub-region curve evolution index and the evolution index of the historical landslide event trajectory library to obtain a highway slope sub-region risk value, comparing the highway slope key sub-region risk value with a preset risk threshold and establishing a risk warning level to realize disaster warning of the highway slope.

2. The Beidou-based highway slope disaster early warning method according to claim 1, characterized in that: The displacement difference calculation on the three-dimensional coordinates in the highway slope node data to obtain the node displacement change trend comprises the following specific steps: The displacement change amount is obtained by displacement difference calculation on the three-dimensional coordinates: ； wherein, a displacement change amount of the i th Beidou receiving node in the t th period, denotes a longitude change amount of the i th Beidou receiving node in the t th period, - , denotes a latitude change amount of the i th Beidou receiving node in the t th period, - , denotes an elevation coordinate change amount of the i th Beidou receiving node in the t th period, - ;​​​ a trend slope of the ith beidou receiving node differential sequence : ； wherein, is the mean of the time series, is the mean of the differential series of the i-th Beidou receiving node, , , t is the t period, and T is the total detection period.​​ The dynamic threshold is calculated by the sliding window method, and w is the sliding window length: ； wherein, denotes the dynamic threshold value of the i-th Beidou receiving node at period t for detecting the impulse point, is a threshold coefficient, and are the mean and standard deviation of the displacement change amount of the sliding window , respectively. The dynamic threshold of the i th Beidou receiving node at period t is calculated, and the pulse point count is calculated: ； wherein, is the total number of impulse points of the i-th Beidou receiving node, denotes the dynamic threshold of the i-th Beidou receiving node at period t, I() is an indicator function, taking 1 when the condition is met, and 0 otherwise, and T is the total monitoring period. The stability feature is calculated: ； wherein, is the overall standard deviation of the displacement amount sequence of the ith Beidou receiving node, t is the t period, and T is the total detection period, is the displacement change amount of the ith Beidou receiving node in the t period, is the mean value of the differential sequence of the ith Beidou receiving node.

3. The road slope disaster early warning method based on Beidou according to claim 2, characterized in that: The statistical analysis on the node displacement change trend to divide the key sub-region category of the highway slope key sub-region comprises the following steps: When the Beidou receiving node satisfies and , then the Beidou receiving node has a persistent deformation feature, wherein, is the trend slope of the differential sequence of the i-th Beidou receiving node, is the trend slope threshold, is the total number of pulse points of the i-th Beidou receiving node, is the pulse point proportion threshold; When the Beidou receiving node satisfies and , then the Beidou receiving node has the intermittent pulse impact feature; When the Beidou receiving node satisfies and and then the Beidou receiving node has a static stability feature, is the overall standard deviation of the displacement sequence of the i-th Beidou receiving node, is a stability threshold value; The feature type quantity proportion of each Beidou receiving node in the highway slope key sub-region is counted, when the proportion of a certain type of node is the highest and exceeds the preset proportion threshold, the sub-region is divided into the corresponding category, and finally the region category of the highway slope key sub-region is divided into the persistent deformation region, the intermittent pulse disturbance region and the static stable region.

4. The road slope disaster early warning method based on Beidou according to claim 3, characterized in that: The feature extraction on the highway slope node data to obtain the highway slope node feature vector comprises the following steps: The displacement speed, displacement direction angle and node collaborative change feature under each period are obtained by the feature extraction on the highway slope node data: ； wherein, is the displacement velocity of the i-th Beidou receiving node in the t-th period, is the displacement change amount of the i-th Beidou receiving node in the t-th period, is the period interval; ； wherein, is a displacement direction angle of the i-th Beidou receiving node in the t period, represents a latitude change amount of the i-th Beidou receiving node in the t period, represents a longitude change amount of the i-th Beidou receiving node in the t period; The node collaborative change feature: ； wherein, represents the displacement similarity of the ith Beidou receiving node and the jth Beidou receiving node, is the displacement change amount of the ith Beidou receiving node at the t period, is the displacement change amount of the jth Beidou receiving node at the t period; ； wherein, is a neighboring node collaborative change feature of the ith Beidou receiving node in the t period, represents the displacement similarity of the ith Beidou receiving node and the jth Beidou receiving node, is a displacement similarity threshold, is a neighboring node collaborative change feature of the ith Beidou receiving node in the t period, is a number of neighboring nodes, is an indicator function, which is 1 when the condition is met, and 0 otherwise. For the i-th Beidou receiving node, the highway slope node feature vector is (t), , ].

5. The road slope disaster early warning method based on Beidou according to claim 4, characterized in that: The similarity between the highway slope node feature vectors in each key sub-region category is calculated, and a highway slope node similarity matrix is constructed, including the following steps: The similarity between the highway slope node feature vectors in each key sub-region category is calculated, and a highway slope node similarity matrix is constructed: ； wherein, is the similarity between the i-th highway slope node feature vector and the j-th highway slope node feature vector in the highway slope node similarity matrix, t is a t period, and T is a total detection period, is the displacement velocity similarity, is the displacement direction angle similarity, is the node cooperative change feature similarity, , and are weights of the displacement velocity similarity, the displacement direction angle similarity, and the node cooperative change feature similarity, respectively.

6. The road slope disaster early warning method based on Beidou according to claim 5, characterized in that: The contour coefficient of the highway slope node trajectory cluster is calculated to obtain a clustering cluster consistency index, including the following steps: The contour coefficient of the highway slope node trajectory cluster is calculated to obtain a clustering cluster consistency index: ； wherein, is a cluster consistency index of the cth cluster of highway slope node trajectory clusters, is the number of highway slope node feature vectors in the cth cluster of highway slope node trajectory clusters, is the silhouette coefficient of the ith highway slope node feature vector.

7. The road slope disaster early warning method based on Beidou according to claim 6, characterized in that: The highway slope node feature vectors in the high-consistency trajectory cluster are reduced in dimension by principal component analysis to obtain highway slope node reduced dimension data, including the following specific steps: The highway slope node feature vectors in the high-consistency trajectory cluster are reduced in dimension by principal component analysis to obtain highway slope node reduced dimension data: ； wherein, represents the highway slope node dimension reduction data of the i th Beidou receiving node in the high-consistency clustering cluster under t period, represents a one-dimensional dimension reduction function of principal component analysis, represents the highway slope node feature vector of the i th Beidou receiving node in the high-consistency clustering cluster under t period. The reduced dimension data of the highway slope node of the high consistency clustering cluster is , =[ , ,..., ]。 8. The road slope disaster early warning method based on Beidou according to claim 7, characterized in that: Based on the highway slope key sub-region type, the highway slope node reduced dimension data is fitted with corresponding trajectory trend, and corresponding key sub-region curve evolution indexes are obtained, including the following specific steps: For the persistent deformation region, an exponential function is fitted by least squares method: ； wherein is an exponential function of the persistent deformation region, , , is a parameter of the exponential function, t is the period of t; For the intermittent pulse disturbance region, a sine triangle function is fitted by fast Fourier transform: ； wherein, is a sinusoidal triangular function of the intermittent pulse perturbation region, is an amplitude of the mth sinusoidal wave, is an angular frequency of the mth sinusoidal wave, is a phase angle of the mth sinusoidal wave, is a constant term of the sinusoidal triangular function; For the static stable region, residual analysis is performed, and a horizontal straight line is fitted: ； wherein, is a horizontal straight line for the static stability region, is a constant corresponding to the horizontal straight line. a key sub-region curve evolution index corresponding to a key sub-region category, =[ , ], =[ , ], = , wherein, is an index of a persistent deformation region, is an index of an intermittent pulse disturbance region, is an index of a static stable region.

9. The road slope disaster early warning method based on Beidou according to claim 8, characterized in that: The Euclidean distance between the key sub-region curve evolution index and the evolution index of the historical landslide event trajectory library is calculated to obtain a highway slope sub-region risk value, including the following specific steps: The Euclidean distance between the key sub-region curve evolution index and the evolution index of the historical landslide event trajectory library is calculated to obtain a highway slope sub-region risk value: ； wherein FX is the risk value of the highway slope sub-area, represents the lth index in the highway slope curve evolution index, YZ=[ , , ] and YZ is the highway slope curve evolution index, is the lth index in the evolution index of the historical landslide event trajectory library, L is the total number of indexes, and l is the index of the lth index.

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