A 3D millimeter wave radar tunnel deformation monitoring method based on displacement relative change rate

Abstract

The present application relates to the technical field of tunnel engineering monitoring, in particular to a 3D millimeter wave radar tunnel deformation monitoring method based on displacement relative change rate; the method comprises the following steps: adopting a 3D millimeter wave radar to collect multiple frames of original point clouds statically, splicing and averaging the original point clouds after filtering and denoising to generate a reference point cloud, fitting a reference surface according to a tunnel structure and calculating a normal reference distance, a reference elevation and a reference local curvature; collecting target point clouds at a preset frequency and registering them to the reference point cloud; designing a normal displacement relative change rate, an elevation displacement relative change rate and a local curvature displacement relative change rate, and obtaining a comprehensive displacement relative change rate by weighted fusion; smoothing the three change rates in the spatial domain and the time domain; setting three-level early warning thresholds, and adopting a multi-algorithm collaborative judgment to determine the deformation state point by point and issue an early warning. The present application weakens the radar background noise and environmental interference, highlights the small deformation of the tunnel surface, and realizes high-sensitivity, multi-parameter tunnel deformation monitoring and hierarchical early warning.

Description

Technical Field

[0001] This invention relates to the field of tunnel engineering monitoring technology, specifically to a 3D millimeter-wave radar method for monitoring tunnel deformation based on the relative rate of displacement change. Background Technology

[0002] As a core infrastructure in transportation, water conservancy, and municipal engineering, the structural stability of tunnels is directly related to operational safety. In particular, long tunnels and tunnels traversing complex geological areas are prone to deformation such as arch subsidence, sidewall bulging, and localized cracking due to changes in geological conditions, vehicle loads, and environmental erosion. If these deformations are not detected in time, they may lead to safety accidents. Achieving high-precision, long-term continuous monitoring of tunnel deformation is crucial to ensuring the safe operation of tunnels. Existing tunnel deformation monitoring methods include displacement gauge monitoring, lidar monitoring, and total station monitoring.

[0003] Displacement gauge monitoring requires contact installation, total station monitoring requires manual operation, and lidar monitoring has certain environmental requirements. 3D millimeter-wave radar has advantages such as resistance to rain and fog, resistance to obstruction, long distance, high precision, and continuous monitoring, and is gradually being applied to the field of tunnel deformation monitoring. However, existing tunnel deformation monitoring based on 3D millimeter-wave radar mostly adopts the absolute displacement monitoring mode, whose background noise is similar in magnitude to the signal of small tunnel deformation. Small deformations are easily submerged by noise, and the monitoring accuracy needs to be improved. In the field of seismology, the relative change rate of wave velocity, by the ratio of the change in wave velocity to the reference wave velocity, can effectively weaken measurement noise and highlight small changes in the medium, and has been widely used in geological medium monitoring. However, this method is suitable for wave velocity monitoring of underground geological media and cannot be directly transferred to displacement monitoring of curved tunnel structures, and lacks a relative change rate algorithm adapted to the characteristics of tunnel deformation.

[0004] Therefore, drawing on the core idea of ​​the relative change rate of seismic wave velocity, designing a tunnel deformation monitoring method based on the relative change rate of displacement that adapts to the characteristics of 3D millimeter-wave radar point clouds and the curved structure of tunnel surfaces, in order to achieve accurate capture of minute deformations and improve anti-interference capabilities, has become an important technical direction in the current field of tunnel monitoring. Summary of the Invention

[0005] The purpose of this invention is to address the problems existing in the background technology by proposing a 3D millimeter-wave radar tunnel deformation monitoring method based on the relative rate of displacement change.

[0006] The technical solution of this invention: a 3D millimeter-wave radar method for monitoring tunnel deformation based on the relative rate of displacement change, comprising the following specific implementation steps: S1. Use 3D millimeter-wave radar to statically acquire multiple frames of original point cloud in the tunnel monitoring area. After statistical filtering and noise reduction, the points are stitched together and averaged to generate a reference point cloud and the coordinates are calibrated. Based on the shape of the tunnel structure, the reference point cloud is fitted to obtain a reference surface mathematical model. The normal reference distance, reference elevation and reference local curvature of each point are calculated. S2. Keep the radar position unchanged, continuously collect the original target point cloud at different times according to the preset frequency, use the same statistical filtering standard as the reference point cloud for noise reduction and coordinate calibration, and register the target point cloud at each time with the reference point cloud through the ICP iterative nearest point algorithm to ensure that the points correspond one-to-one. S3, the relative change rate of design normal displacement, relative change rate of elevation displacement and relative change rate of local curvature displacement are combined by weighted summation after introducing weight coefficients to obtain the comprehensive relative change rate of displacement. S4. For the calculation results of the three relative displacement change rates, spatial domain smoothing and time domain smoothing are performed respectively. In the spatial domain, the neighborhood point averaging algorithm is used to weaken local random noise, and in the time domain, the moving average window is used to suppress noise jitter. After smoothing, the reduction of standard deviation and the correlation coefficient of deformation trend are verified. S5. Three-level early warning thresholds are set for the three relative rates of displacement and the comprehensive rate of change. The principle of multi-algorithm collaborative judgment is adopted to determine the stable, early warning or dangerous state point by point and area by area and issue corresponding early warning signals. The rate of change data is recorded to draw trend curves. The monitoring frequency is adjusted and the deformation is tracked for areas of continuous deformation.

[0007] Preferably, in step S1, the static acquisition of multiple frames of original point cloud adopts a set acquisition frequency and number of acquisition frames; When using statistical filtering for noise reduction, set thresholds for the number of neighboring points and distance. Based on the actual structural shape of the tunnel arch and sidewalls, circular surface, ellipsoidal surface or polynomial surface algorithms are used for fitting. During the fitting process, the 3σ criterion is used to remove outliers that deviate too far from the fitted surface, and the fitting error is controlled within the set range.

[0008] Preferably, the preset monitoring frequency in step S2 is a set time interval; During registration, the number of iterations is set and robust optimization is introduced to eliminate registration outliers, and the registration error is controlled within the set range.

[0009] Preferably, the formula for calculating the relative rate of change of normal displacement in step S3 incorporates a weighting coefficient, which is adjusted according to the point cloud density. The formula for calculating the relative rate of change of elevation displacement introduces a weighting coefficient; the formula for calculating the relative rate of change of local curvature displacement introduces a weighting coefficient. The comprehensive relative displacement change rate is obtained by weighted summation of the three relative displacement change rates, with each weight adjusted according to the key points of tunnel monitoring.

[0010] Preferably, during spatial domain smoothing in step S4, the neighborhood point averaging is performed using grids of different sizes for the three relative rates of change of displacement. When smoothing in the time domain, the average value is calculated using a sliding window with different frame numbers for each of the three relative rates of change of displacement.

[0011] Preferably, the standard for post-smoothing verification in step S4 is: The standard deviation decreases by a set percentage after smoothing, and the correlation coefficient of the rate of change before and after smoothing meets the set requirements; If the verification fails, adjust the grid size or the number of window frames and reprocess.

[0012] Preferably, in step S5, the three-level warning thresholds are set as normal threshold, warning threshold, and danger threshold for the relative change rate of normal displacement, relative change rate of elevation displacement, relative change rate of local curvature displacement, and relative change rate of comprehensive displacement, respectively.

[0013] Preferably, the multi-algorithm collaborative judgment principle in step S5 is as follows: When the relative rates of change of the three displacements and the combined rate of change are all within the normal threshold, it is determined to be a stable state. When any rate of change or the combined rate of change is at the warning threshold, it is determined to be in a warning state and a warning signal is issued. When any one rate of change or the combined rate of change is at a dangerous threshold, it is determined to be a dangerous state and a danger warning signal is issued.

[0014] Preferably, after recording the rate of change data and plotting the trend curve in step S5, the monitoring frequency for the continuously deformed area is adjusted to a higher frequency to track deformation changes and provide data support for emergency response; once the deformation tends to stabilize, it is determined to be in a stable stage.

[0015] Compared with the prior art, the above-mentioned technical solution of the present invention has the following beneficial technical effects: This invention designs a 3D millimeter-wave radar method for monitoring tunnel deformation based on the relative rate of change of displacement. Drawing on the core idea of ​​the relative rate of change of seismic wave velocity, it uses the ratio of deformation to a baseline quantity as the monitoring index. This effectively weakens the influence of radar background noise, environmental clutter, and interference factors such as temperature vibration, significantly improving the sensitivity to identify minute tunnel deformations. It can capture weak signals in the early stages of deformation, gaining valuable time for tunnel structural safety assessment. For the curved surface structures of the tunnel arch and sidewalls, this invention specifically designs three complementary indices: the relative rate of change of normal displacement, the relative rate of change of elevation displacement, and the relative rate of change of local curvature displacement. These are used to capture local deformation in the normal direction of the curved surface, the overall settlement trend, and hidden damage such as cracking and voiding, respectively. The weighted fusion method yields the comprehensive relative displacement change rate, achieving multi-dimensional deformation characterization from local to global and from surface to interior. A smoothing strategy combining spatial domain neighborhood averaging and time domain sliding windows effectively suppresses random noise and fluctuations while preserving true deformation trend characteristics, ensuring the stability and reliability of monitoring data. Based on this, a three-level early warning threshold is set according to the tunnel structure material and design bearing capacity. A multi-algorithm collaborative judgment principle is used to determine stable, warning, or dangerous states point-by-point and area-by-area, avoiding false alarms and improving the accuracy of early warnings. This invention requires no target or reflector deployment throughout the entire process, is easy to install and maintain, and can operate automatically for extended periods, providing a non-contact, highly sensitive, multi-parameter comprehensive deformation monitoring method for tunnel engineering. Attached Figure Description

[0016] Figure 1 This is a flowchart of a 3D millimeter-wave radar tunnel deformation monitoring method based on the relative rate of displacement change proposed in this invention. Detailed Implementation

[0017] Example 1, as Figure 1 As shown, the present invention proposes a 3D millimeter-wave radar method for monitoring tunnel deformation based on the relative rate of displacement change, which includes the following specific implementation steps: S1. Use 3D millimeter-wave radar to statically acquire multiple frames of original point cloud in the tunnel monitoring area. After statistical filtering and noise reduction, stitch them together and take the average to generate a reference point cloud and calibrate the coordinates. Based on the actual structural shape of the tunnel arch and sidewalls, use circular surface, ellipsoidal surface or polynomial surface algorithm to fit the reference point cloud. After removing outliers, output the reference surface mathematical model and calculate the normal reference distance, reference elevation and reference local curvature of each point. S2. Keep the radar position unchanged and continuously collect the original target point cloud at different times according to the preset frequency. Use the same statistical filtering standard as the reference point cloud for noise reduction and coordinate calibration. Use the ICP iterative nearest point algorithm to accurately register the target point cloud with the reference point cloud at each time. Introduce robust optimization to remove outliers to ensure that the reference point and the target point correspond one-to-one and eliminate point cloud misalignment caused by tunnel vibration and temperature drift. S3. Drawing on the concept of relative change rate of seismic wave velocity, three algorithms for relative change rate of displacement are designed: relative change rate of normal displacement is used to capture small deformations in the normal direction of the surface, relative change rate of elevation displacement is used to monitor overall settlement, and relative change rate of local curvature displacement is used to discover hidden damage. After optimization by introducing weight coefficients, the comprehensive relative change rate of displacement is obtained by weighted summation, which weakens the background noise and highlights the signal of small deformation. S4. For the calculation results of the three relative rates of change of displacement, spatial domain smoothing and time domain smoothing are performed respectively: in the spatial domain, the neighborhood point averaging algorithm with different grid sizes is used to weaken local random noise, and in the time domain, the moving average window with different frame numbers is used to suppress noise jitter; after smoothing, the results are verified to ensure that the standard deviation is reduced and the deformation trend correlation coefficient meets the requirements. If the verification fails, the parameters are adjusted and the process is repeated. S5. Based on the tunnel structure material, design bearing capacity, and radar background noise level, three-level early warning thresholds are set for the three relative displacement change rates and the comprehensive change rate. Using the principle of multi-algorithm collaborative judgment, the stable, early warning, or dangerous state is determined point by point and area by area, and corresponding early warning signals are issued. Change rate data is recorded to draw trend curves, and the monitoring frequency is adjusted and the deformation is tracked for areas of continuous deformation to provide data support for emergency response.

[0018] It should be noted that the following embodiments use a tunnel in Gaosheng, Chongqing (circular arch, twin tunnels, single line, complex geology, with risks such as large deformation of soft rock and sudden water inrush) as the monitoring object, and use a 77GHz 3D millimeter wave radar (range accuracy ±0.5mm~±1cm, monitoring distance ±25m) to achieve accurate monitoring of small deformations of the tunnel arch.

[0019] In a specific embodiment, step S1 involves acquiring the reference point cloud and fitting the reference surface, specifically as follows: S11. Fix the 77GHz 3D millimeter-wave radar at a preset position on the tunnel sidewall to ensure that the radar scanning range completely covers the tunnel monitoring area (including the arch and sidewall); after installation, keep the radar position unchanged, adopt the static acquisition mode, and continuously acquire multiple frames of the original point cloud of the tunnel monitoring area. The acquisition frequency is 1 frame / second, and the number of frames acquired is not less than 10 frames. In this embodiment, 10 frames are acquired. S12. Perform noise reduction preprocessing on the acquired raw point cloud, specifically including: A statistical filtering algorithm is used, with a threshold for the number of neighboring points set (8 in this embodiment) and a distance threshold set (0.2m in this embodiment) to delete isolated background clutter points and flying points, while retaining the main point cloud of the tunnel structure. The point clouds after denoising from multiple frames are stitched together, and the average value of the coordinates of each point after stitching is taken as the reference point cloud for the tunnel, which initially reduces the impact of the background noise of 3D millimeter-wave radar on the reference point cloud. The reference point cloud is calibrated using a local coordinate system to ensure the uniformity and accuracy of the coordinate data. S13. Based on the actual structural shape of the tunnel monitoring area (in this embodiment, the arch is a circular arch), the corresponding surface fitting algorithm is used to fit the reference point cloud: The circular arch is fitted using a circular surface fitting algorithm; During the fitting process, the 3σ criterion is used to remove outliers that deviate too far from the fitted surface, ensuring the fit between the reference surface and the actual tunnel structure, and the fitting error is controlled within ±0.1mm. After fitting is complete, the mathematical model of the reference surface is output; S14. Calculate the core reference parameters for each point in the reference point cloud, specifically including: Reference distance along the normal of the reference surface The normal direction is the perpendicular direction of the reference surface at that point. The gradient descent method is used to calculate the normal vector direction. The side of the tunnel structure facing the radar is set as the positive direction, and the point is located on that side. Positive values ​​are taken, and negative values ​​are taken otherwise; in this embodiment The range is 0.5~1.2m, with an average value of 0.85m; Baseline elevation value The coordinate values ​​of each reference point along the Z-axis of the coordinate system, in this embodiment... The range is 25.3~26.1m, with an average of 25.7m; Reference Local Curvature The surface fitting derivative method is used, which obtains the second derivative of the reference surface. The sign of the curvature reflects the direction of the surface curvature, and the absolute value reflects the degree of curvature. In this embodiment... The range is 0.008~0.012m -1 The average value is 0.01m. -1 .

[0020] In a specific embodiment, step S2 involves target point cloud acquisition and registration, specifically as follows: S21. Keep the 3D millimeter-wave radar installation position unchanged and continuously collect the original target point cloud at different times in the tunnel monitoring area according to the preset monitoring frequency. In this embodiment, the monitoring frequency is set to 1 time / 10 minutes, and the data is continuously collected for 30 days, with 144 frames per day. S22. For the original target point cloud at each time point, adopt the same denoising preprocessing standard as the baseline point cloud: The same statistical filtering algorithm (neighborhood point number threshold of 8, distance threshold of 0.2m) is used to remove background clutter points and flying points, and retain the main target point cloud of the tunnel. The target point cloud is calibrated to use the same local coordinate system as the reference point cloud to eliminate calculation errors caused by coordinate deviation. S23. The ICP (Iterative Closest Point) registration algorithm is used to register the target point cloud with the reference point cloud at each time step. Set the number of iterations (50 in this embodiment), introduce robust optimization, eliminate registration outliers, and ensure that the reference point and the target point correspond one-to-one; The registration error is controlled within ±0.05mm to avoid point cloud misalignment caused by slight tunnel vibration and temperature drift.

[0021] In one specific embodiment, step S3 draws on the core logic of the relative change rate of seismic wave velocity and, combined with the characteristics of the tunnel's curved surface structure, designs three algorithms for the relative change rate of displacement. By using the ratio of the displacement change to the reference displacement, it weakens background and environmental noise and highlights minute deformations. Specifically: S31. Based on the registered target point cloud and reference point cloud, find the target point corresponding to each reference point and calculate three core real-time parameters: Real-time distance of the target point along the normal of the reference surface , The rules for determining positive and negative signs and Consistent; Real-time elevation value of the target point ; Real-time local curvature at the location of the target point Calculation method and Consistent; S32. Calculate the relative rate of change of normal displacement to adapt to the deformation characteristics of the tunnel surface and accurately capture the minute deformations of the tunnel structure along the normal direction of the surface (such as subsidence and bulges). The formula is: ; In the formula, The relative rate of change of normal displacement; To prevent the zero-correction term; Introducing weighting coefficients The value ranges from 0.7 to 0.9, and is adjusted according to the point cloud density; the denser the point cloud, the higher the value. The larger the value, the better the optimized formula becomes: ; S33. Calculate the relative rate of change of elevation displacement, adapting to overall tunnel settlement monitoring, simplifying the calculation process. The formula is: ; In the formula, This represents the relative rate of change of elevation displacement; Introducing weighting coefficients The range is 0.5~0.7, and the optimized formula is: ; S34. Calculate the relative rate of change of local curvature displacement, which is more sensitive than the simple rate of change of displacement, and is suitable for monitoring hidden deformations such as local cracking and voids in tunnels. The formula is: ; In the formula, This represents the relative rate of change of local curvature displacement; Introducing weighting coefficients The range is 0.8~1.0, and the optimized formula is: ; S35. Using a weighted summation method, the calculation results of the three relative displacement change rates are combined to obtain the final comprehensive relative displacement change rate R: ; It should be noted that the weighting can be flexibly adjusted according to the focus of tunnel monitoring (e.g., if the focus is on monitoring local damage, the weighting can be increased). (weight) It should be further noted that, under the stable state of the tunnel, the calculations obtained in this embodiment are... The fluctuation is within ±0.0005. The fluctuation is within ±0.0008. Fluctuations are within ±0.001, and R fluctuations are within ±0.0006, which can clearly capture minute deformations at the 0.1mm level.

[0022] In a specific embodiment, step S4 designs a targeted spatiotemporal smoothing process for the calculation results of the three relative rates of displacement, suppressing the background noise of 3D millimeter-wave radar while avoiding distortion of deformation signals. Specifically: S41. Using the neighborhood point averaging algorithm, the neighborhood range is adjusted according to the characteristics of the three algorithms: Using a 5x5 grid, Using a 3×3 grid, Use a 7×7 grid; Calculate the average rate of change of each point and its surrounding neighboring points to reduce local random noise; It should be noted that in this embodiment, the standard deviation is reduced by 40% to 45% after spatial smoothing. S42. Using the moving average window algorithm: and Use a 3-frame window. Use a 5-frame window; Calculate the average of the smoothed rate of change at different times for the same monitoring point to suppress noise and jitter in the time dimension and improve data stability; It should be noted that in this embodiment, the time jitter is reduced by more than 50% after time smoothing; S43. Calculate the standard deviation of the three rates of change before and after smoothing, ensuring that the standard deviation is reduced by 30% to 50% after smoothing; Calculate the correlation coefficient of the rate of change before and after smoothing, and ensure that the correlation coefficient is ≥0.95 to ensure that the deformation trend remains unchanged; In this embodiment, the correlation coefficient before and after smoothing is ≥0.96, the deformation trend remains unchanged, and the monitoring requirements are met; If the verification fails, adjust the smoothing parameters (such as grid size and window frame count) and reprocess.

[0023] In a specific embodiment, step S5 involves determining the deformation state and providing a graded early warning, specifically as follows: S51. Based on the tunnel structure material, design bearing capacity, and the background noise level of 3D millimeter-wave radar, three levels of early warning thresholds are set for the three relative rates of displacement change and the comprehensive rate of change (which can be adjusted according to the actual engineering scenario). This embodiment uses the following threshold: (1) Relative rate of change of normal displacement : normal( ≤0.001), Warning (0.001 < ≤0.005), Danger ( >0.005); (2) Relative rate of change of elevation displacement : normal( ≤0.002), Warning (0.002 < ≤0.006), Dangerous (>0.006); (3) Relative rate of change of local curvature displacement : normal( ≤0.003), warning (0.003 < ≤0.007), Danger ( >0.007); (4) Overall relative displacement change rate R: Normal ( ≤0.0015), Warning (0.0015 < ≤0.0055), Danger ( >0.0055); S52. Employing a multi-algorithm collaborative judgment principle, the tunnel deformation state is determined point-by-point and region-by-region: (1) Steady state: All three rates of change and the overall rate of change are within the normal threshold, indicating no obvious deformation; (2) Warning status: When any rate of change or the combined rate of change is at the warning threshold, it is determined that a small deformation has occurred and a warning signal is issued; (3) Dangerous state: If any one rate of change or the combined rate of change is at the danger threshold, it is determined that the deformation is aggravated and a danger warning signal is issued; In this embodiment, all rates of change were within the normal threshold for the first 24 days, and the overall dome remained stable; on the 25th day, a certain area... =-0.002 (reaching the warning threshold), R=-0.0018 (reaching the warning threshold), issue a warning signal; S53. Record the rate of change data at each moment, plot the change curve, and analyze the deformation development trend; for areas with continuous deformation, adjust the monitoring frequency, track deformation changes, and provide data support for emergency response. In this embodiment, after the warning signal was issued, the monitoring frequency was adjusted to once every 2 minutes. On-site investigation revealed slight subsidence in the area, and reinforcement measures were taken. By the 29th day, the change rates tended to stabilize, and the deformation was determined to have entered a stable stage, verifying the effectiveness of the method.

[0024] The embodiments of the present invention have been described in detail above with reference to the accompanying drawings. However, the present invention is not limited thereto. Various changes can be made within the scope of knowledge possessed by those skilled in the art without departing from the spirit of the present invention.

Claims

1. A 3D millimeter-wave radar method for monitoring tunnel deformation based on the relative rate of displacement change, characterized in that, The specific implementation steps include the following: S1. Use 3D millimeter-wave radar to statically acquire multiple frames of original point cloud in the tunnel monitoring area. After statistical filtering and noise reduction, the points are stitched together and averaged to generate a reference point cloud and the coordinates are calibrated. Based on the shape of the tunnel structure, the reference point cloud is fitted to obtain a reference surface mathematical model. The normal reference distance, reference elevation and reference local curvature of each point are calculated. S2. Keep the radar position unchanged, continuously collect the original target point cloud at different times according to the preset frequency, use the same statistical filtering standard as the reference point cloud for noise reduction and coordinate calibration, and register the target point cloud at each time with the reference point cloud through the ICP iterative nearest point algorithm to ensure that the points correspond one-to-one. S3, the relative change rate of design normal displacement, relative change rate of elevation displacement and relative change rate of local curvature displacement are combined by weighted summation after introducing weight coefficients to obtain the comprehensive relative change rate of displacement. S4. For the calculation results of the three relative displacement change rates, spatial domain smoothing and time domain smoothing are performed respectively. In the spatial domain, the neighborhood point averaging algorithm is used to weaken local random noise, and in the time domain, the moving average window is used to suppress noise jitter. After smoothing, the reduction of standard deviation and the correlation coefficient of deformation trend are verified. S5. Three-level early warning thresholds are set for the three relative rates of displacement and the comprehensive rate of change. The principle of multi-algorithm collaborative judgment is adopted to determine the stable, early warning or dangerous state point by point and area by area and issue corresponding early warning signals. The rate of change data is recorded to draw trend curves. The monitoring frequency is adjusted and the deformation is tracked for areas of continuous deformation.

2. The 3D millimeter-wave radar tunnel deformation monitoring method based on the relative rate of displacement change according to claim 1, characterized in that, In step S1, the static acquisition of multiple frames of raw point cloud data uses a set acquisition frequency and number of frames. When using statistical filtering for noise reduction, set thresholds for the number of neighboring points and distance. Based on the actual structural shape of the tunnel arch and sidewalls, circular surface, ellipsoidal surface or polynomial surface algorithms are used for fitting. During the fitting process, the 3σ criterion is used to remove outliers that deviate too far from the fitted surface, and the fitting error is controlled within the set range.

3. The 3D millimeter-wave radar tunnel deformation monitoring method based on the relative rate of displacement change according to claim 2, characterized in that, In step S2, the preset monitoring frequency is the set time interval; During registration, the number of iterations is set and robust optimization is introduced to eliminate registration outliers, and the registration error is controlled within the set range.

4. The 3D millimeter-wave radar tunnel deformation monitoring method based on the relative rate of displacement change according to claim 3, characterized in that, In step S3, the formula for calculating the relative rate of change of normal displacement introduces a weighting coefficient, which is adjusted according to the point cloud density. The formula for calculating the relative rate of change of elevation displacement introduces a weighting coefficient; the formula for calculating the relative rate of change of local curvature displacement introduces a weighting coefficient. The comprehensive relative displacement change rate is obtained by weighted summation of the three relative displacement change rates, with each weight adjusted according to the key points of tunnel monitoring.

5. The 3D millimeter-wave radar tunnel deformation monitoring method based on the relative rate of displacement change according to claim 4, characterized in that, In step S4, during spatial domain smoothing, neighbor point averaging is performed using grids of different sizes for the three relative rates of change of displacement. When smoothing in the time domain, the average value is calculated using a sliding window with different frame numbers for each of the three relative rates of change of displacement.

6. The 3D millimeter-wave radar tunnel deformation monitoring method based on the relative rate of displacement change according to claim 5, characterized in that, The criteria for post-smoothing verification in step S4 are: The standard deviation decreases by a set percentage after smoothing, and the correlation coefficient of the rate of change before and after smoothing meets the set requirements; If the verification fails, adjust the grid size or the number of window frames and reprocess.

7. The 3D millimeter-wave radar tunnel deformation monitoring method based on the relative rate of displacement change according to claim 6, characterized in that, In step S5, the three-level early warning thresholds are set as normal threshold, early warning threshold, and danger threshold for the relative change rate of normal displacement, relative change rate of elevation displacement, relative change rate of local curvature displacement, and relative change rate of comprehensive displacement, respectively.

8. The 3D millimeter-wave radar tunnel deformation monitoring method based on the relative rate of displacement change according to claim 7, characterized in that, The specific principle of multi-algorithm collaborative judgment in step S5 is as follows: When the relative rates of change of the three displacements and the combined rate of change are all within the normal threshold, it is determined to be a stable state. When any rate of change or the combined rate of change is at the warning threshold, it is determined to be in a warning state and a warning signal is issued. When any one rate of change or the combined rate of change is at a dangerous threshold, it is determined to be a dangerous state and a danger warning signal is issued.

9. The 3D millimeter-wave radar tunnel deformation monitoring method based on the relative rate of displacement change according to claim 8, characterized in that, After recording the rate of change data and plotting the trend curve in step S5, the monitoring frequency for the continuously deformed area is adjusted to a higher frequency to track deformation changes and provide data support for emergency response; once the deformation tends to stabilize, it is determined to be in a stable phase.

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