Tunnel vault settlement calculation and early warning method with coupling space minimum distance constraint

Abstract

This invention relates to a method for calculating and early warning of tunnel arch settlement coupled with minimum spatial distance constraints, applicable to deformation monitoring and safety early warning during tunnel construction. The method includes: setting up at least five observation points on the same cross-section of the tunnel, obtaining the relative three-dimensional coordinates of each observation point under multiple observation periods; setting a candidate set of stable points including all observation points except the arch apex, and selecting the three points with the lowest scores to form the current stable point set; constructing an objective function based on the current stable point set that integrates the stable point registration residual and the minimum spatial distance constraint, solving for the rigid body parameters of observation period k, and using the rigid body parameters to calculate the de-rigidity displacement of all observation points on the cross-section; obtaining the local unit normal vector of each observation point based on the arch shape fitting of the reference period cross-section, and projecting the de-rigidity displacement onto the Z-axis and normal directions respectively to obtain the Z-axis settlement and normal settlement of each observation point.

Description

Technical Field

[0001] This invention relates to a method for calculating and providing early warning of tunnel arch settlement based on minimum distance constraints in coupled space. It is applicable to deformation monitoring and safety early warning during tunnel construction. Background Technology

[0002] During the tunnel construction phase, various on-site factors, such as blasting and excavation at the tunnel face, changes in initial support, traffic organization within the tunnel, and light obstruction, make it difficult to stably establish external control points within the tunnel. Traditional methods for calculating tunnel crown settlement are based on the construction of a control network and rely heavily on the stability of external benchmarks. If the external benchmarks drift or become unreachable due to construction conditions, traditional methods will transmit inaccurate rigid body deformations to the settlement calculation results, severely affecting the accuracy of crown settlement calculations and failing to accurately reflect the actual deformation state of the tunnel structure.

[0003] Meanwhile, traditional methods lack a safety early warning system deeply coupled with settlement calculations. The early warning thresholds are mostly fixed values, which cannot adapt to the actual fluctuation characteristics of settlement data and are prone to false alarms and missed alarms. Moreover, in the face of the common situation of missing measurement points during construction, traditional calculation methods do not have an effective fault-tolerant processing mechanism, which can easily lead to the interruption of the settlement calculation sequence, further affecting the reliability of subsequent early warning judgments and making it difficult to meet the actual engineering needs of deformation monitoring and safety early warning during tunnel construction. Summary of the Invention

[0004] The technical problem to be solved by the present invention is to provide a method for calculating and early warning of tunnel arch settlement with coupling spatial minimum distance constraints, in order to address the above-mentioned problems.

[0005] The technical solution adopted in this invention is: a method for calculating tunnel arch settlement with coupled spatial minimum distance constraints, comprising: S100. Set up at least five observation points on the same cross section of the tunnel, including the top of the arch, the left and right middle layer points and the left and right lower layer points, and obtain the relative three-dimensional coordinates of each observation point under multiple observation periods. S200. Set the candidate set of stable points to include all observation points except the apex of the arch. For any observation period k after the reference period k0, calculate the stable point score of each point in the candidate set by quantifying the change in the Euclidean distance between the point pairs containing the points to be scored relative to the reference period k0. Select the three points with the smallest scores to form the stable point set for the current period. S300. Based on the current stable point set, construct an objective function that integrates the stable point registration residual and the minimum spatial distance constraint, solve for the rigid body parameters of the observation period k, and use the rigid body parameters to calculate the de-rigid body displacement of all observation points of the section. S400. Based on the arch fitting of the reference section, the local unit normal vector of each observation point is obtained. The rigid body displacement is projected onto the Z-axis direction and the normal direction respectively, and the Z-direction settlement and normal settlement of each observation point are obtained respectively.

[0006] By employing the aforementioned technical means, settlement calculation is achieved through the multi-period relative three-dimensional coordinates of a limited number of measuring points within the cross-section, eliminating the dependence on external control points. A virtual reference system within the cross-section is constructed by identifying stable points, and a rigid body fitting method with minimum spatial distance constraints is used to remove the overall non-real rigid body deformation of the cross-section, extracting only the local real deformation displacement. Simultaneously, the settlement data in both the Z-direction and normal direction are output to achieve cross-validation of the settlement results, significantly improving the accuracy of the arch settlement calculation and adapting to tunnel construction conditions without external references.

[0007] As a preferred embodiment, the step of calculating the stable point score of each point in the candidate set by quantifying the change in the Euclidean distance between point pairs containing the points to be scored relative to the reference period k0 includes: ; Where u and v are points in the candidate set, and C is the stable point candidate set. , Let u and v be the three-dimensional coordinates of point k during the observation period. , The reference period is defined by the three-dimensional coordinates of points u and v at point k0.

[0008] By employing the aforementioned technical means and taking the reference period as a benchmark, the stability of candidate points is characterized by the sum of changes in the Euclidean distance between point pairs. This achieves the quantification and standardization of stable point selection, avoids the subjectivity of manual selection, improves the accuracy of stable point identification, and provides a reliable basis for the construction of a virtual benchmark system.

[0009] As a preferred embodiment, the selection of the three points with the lowest scores to form the current stable point set includes:

[0010] If there are ties in the scores, multiple candidate triplets for stable points are formed. The shape preservation index of each candidate triplet is calculated by quantifying the change of each point in the triplet with respect to the Euclidean distance relative to the reference period k0. The triplet with the smallest index is selected as the final stable point set.

[0011] By employing the aforementioned technical means, the evaluation method is upgraded from single-point stability assessment to overall geometric stability assessment of the stable point set. This ensures that the selected stable point set maintains a geometric shape consistent with the reference period, avoiding situations where a single point is stable but the overall geometry is distorted, thereby further improving the stability of the virtual reference system.

[0012] As a preferred embodiment, the step of calculating the shape preservation index of each candidate triplet by quantifying the change in Euclidean distance of each point in the triplet relative to the reference period k0 includes: ; in, ω is the shape preservation index of candidate triple S at observation period k; S is the stable candidate triple; ij Point-to-point weights; , Let i and j be the three-dimensional coordinates of points i and j during the observation period k. , Let i and j be the three-dimensional coordinates of points i and j in the reference period k0.

[0013] By employing the aforementioned technical means, the influence of distance deviation is amplified through a weighted sum of squares, while simultaneously eliminating the offsetting effect of positive and negative deviations. This allows for the precise quantification of the geometric consistency of candidate triplets for stable points, providing a quantitative standard for the verification of stable point sets when scores are tied. Furthermore, this indicator can be used as a quality diagnostic metric for subsequent rigid body fitting constraints, thereby achieving the linkage between stable point screening and rigid body fitting.

[0014] As a preferred embodiment, step S200 includes: If the improvement of the current period's shape retention index or stable point registration residual compared to the previous period is less than the preset value, then the stable point set of the previous period will be used directly.

[0015] By employing the aforementioned technical means, stable point anti-shaking processing is achieved, avoiding frequent switching of the stable point set due to minor fluctuations in the observed data. This reduces unnecessary fluctuations in rigid body fitting and settlement calculation, improves the continuity and stability of the settlement calculation sequence, and simultaneously reduces the computational load, thus adapting to the rapid solution requirements of engineering sites.

[0016] As a preferred embodiment, the objective function for constructing the fusion of stable point registration residuals and spatial minimum distance constraints based on the current stable point set includes: ; Where, ω i α represents the stability point weight; α represents the spatial minimum distance constraint strength; S represents the current stability point set. Let i be the three-dimensional coordinates of point i during the observation period k. J represents the three-dimensional coordinates of point i at reference period k0; S (k) is the shape preservation index of the stable point set, and is the quantization term of the minimum spatial distance constraint; rigid body parameters include the rotation matrix R. k Translation vector t k .

[0017] By employing the aforementioned technical means, a multi-constraint rigid body registration objective function is constructed, which integrates the stable point registration residual with the minimum spatial distance constraint. This achieves alignment of the stable point sets during the observation and reference periods while forcibly ensuring the geometric rigidity of the stable point sets remains unchanged. This effectively suppresses geometric distortion caused by proportional drift and shear deviation during rigid body fitting, improves the accuracy of rigid body parameter solving, and thus ensures the authenticity of rigid body displacement calculation.

[0018] As a preferred embodiment, the solution for obtaining the rigid body parameters for the observation period k includes: First, calculate the stable point set. During the observation period The weighted centroid of the reference period k0 and the weighted centroid of the reference period k0; Based on stable point set During the observation period The stable coordinates and weighted centroids of the reference period k0 are used to construct the covariance matrix; Singular value decomposition is performed on the covariance matrix to obtain the initial rotation matrix, and the initial translation vector is then calculated based on the initial rotation matrix. Based on the initial rigid body parameters, the objective function is iteratively optimized using the iterative reweighted least squares method. The stable point weights are updated and the shape preservation index is linearized. The rotation matrix and translation vector are alternately minimized and updated until the convergence criterion is met, and the final rigid body parameters are obtained.

[0019] Using the above-mentioned technical means, a two-step solution method of "weighted SVD closed-loop initialization + iterative reweighted least squares optimization" is adopted. Weighted SVD can quickly obtain high-quality initial rigid body parameters and reduce the number of iterations. Iterative reweighted least squares can reduce the influence of gross errors on the fitting results. By controlling the iteration accuracy through convergence criteria, high-precision and high-stability solutions for rigid body parameters are achieved, providing a reliable foundation for rigid body displacement calculation.

[0020] As a preferred option, a missing test tolerance processing step is also included: When the number of valid observation points in the candidate stable point set is less than 3, if there are 3 valid points remaining, the solution is performed directly using these 3 points as the stable point set; if there are 2 valid points remaining, the rigid body parameters from the previous period are introduced as historical constraints for joint solution; if the number of valid points remaining is ≤1, the current solution is terminated and the missing measurement information is recorded.

[0021] As a preferred option, a data reinjection step is also included: When a missing observation point is restored to observation, it is assigned a weight of 0.5 in the first period after restoration, the weight is increased to 0.8 in the second period, and the weight is restored to 1.0 in the third period; the weight adjustment is only made for the restored point itself.

[0022] By employing the aforementioned technical means, the weights are gradually reinjected after the missing measurement points are restored, avoiding abrupt changes in settlement calculation results due to abnormal initial observation data of the restored points, ensuring a smooth transition of the settlement sequence, and adjusting the weights only for the restored points themselves without affecting the stable calculation of other measurement points, thereby further improving the continuity of the calculation results.

[0023] A tunnel arch settlement calculation device with coupled spatial minimum distance constraints, comprising: The data management module is used to set up at least five observation points on the same cross section of the tunnel, including the top of the arch, the left and right middle layer points, and the left and right lower layer points, and to obtain the relative three-dimensional coordinates of each observation point under multiple observation periods; The stable point identification module is used to set the stable point candidate set to include all observation points except the apex of the arch. For any observation period k after the reference period k0, the stable point score of each point in the candidate set is calculated by quantifying the change in the Euclidean distance between the point pairs containing the points to be scored relative to the reference period k0. The three points with the smallest scores are selected to form the stable point set for the current period. The rigid body fitting module is used to construct an objective function that integrates the registration residuals of stable points and the minimum spatial distance constraint based on the current stable point set, solve for the rigid body parameters of the observation period k, and use the rigid body parameters to calculate the de-rigid body displacement of all observation points of the section. The settlement extraction module is used to obtain the local unit normal vector of each observation point based on the arch fitting of the cross section during the reference period, and to project the rigid body displacement onto the Z-axis direction and the normal direction respectively, so as to obtain the Z-axis settlement and normal settlement of each observation point respectively.

[0024] A storage medium storing a computer program executable by a processor, wherein the computer program, when executed, implements the steps of the tunnel arch settlement calculation method.

[0025] A tunnel arch settlement calculation device has a memory and a processor. The memory stores a computer program that can be executed by the processor. When the computer program is executed, it implements the steps of the tunnel arch settlement calculation method.

[0026] A method for early warning of tunnel arch settlement includes: Based on the tunnel arch settlement calculation method, the Z-axis settlement and normal settlement of each observation point on the same cross section of the tunnel under multiple observation periods are calculated. Set a sliding window, and within the sliding window, calculate the standard deviation of the settlement sequence increment for each observation point. The settlement sequence is a sequence composed of the Z-axis settlement or normal settlement of each observation point in multiple periods within the sliding window. Based on the standard deviation of the settlement sequence increment at each observation point, a single-point early warning threshold and a linkage early warning threshold between adjacent observation points are constructed for each observation point. By combining the Z-axis settlement, normal settlement, and adaptive early warning threshold, and overlaying settlement trend criteria, a graded early warning judgment is made on the settlement risk of the tunnel arch.

[0027] Through the above technical means, an arch settlement early warning system is achieved that is deeply coupled with the settlement calculation method. The early warning data comes directly from the settlement calculation results of this invention, ensuring the authenticity of the early warning basis. The standard deviation is calculated by sliding window to quantify the fluctuation of settlement data, construct an adaptive early warning threshold, and superimpose trend criteria to achieve hierarchical early warning, avoiding the false alarm and missed alarm problems of fixed thresholds, and improving the reliability and pertinence of the early warning.

[0028] As a preferred embodiment, the calculation of the standard deviation of the settlement sequence increment at each observation point includes: ; in, Let W be the standard deviation of the settlement sequence at the i-th observation point; W be the sliding window; |W| be the number of observation periods within the sliding window; The settlement of measuring point i during the observation period k within the sliding window; Let be the average settlement of measurement point i within the sliding window.

[0029] As a preferred embodiment, the calculation formula for the single-point early warning threshold includes: ; The formula for calculating the linkage early warning threshold is: ; in, Let be the single-point early warning threshold for the i-th observation point; is the linkage warning threshold between observation point i and observation point j; c is the threshold coefficient; , denoted as the standard deviations of the settlement sequences at observation points i and j, respectively.

[0030] As a preferred option, the CUSUM test and short-term prediction extrapolation are used, wherein the CUSUM test is used to capture the offset of the cumulative sum of settlement increments, and the short-term prediction extrapolation includes using an autoregressive model AR(1) or Kalman filtering to make short-term predictions on the settlement sequence.

[0031] By using the above technical means, the trend of settlement is captured by CUSUM test, and the short-term prediction extrapolation of settlement is achieved by AR(1) or Kalman filtering. The risk of continuous deterioration of settlement is identified, and the early warning is upgraded from "passive over-limit alarm" to "active trend early warning", which effectively reduces the probability of missed reporting and provides an early decision basis for tunnel construction safety management.

[0032] The beneficial effects of this invention are as follows: This invention addresses the core problems of the difficulty in stably setting up external control points in tunnel construction and the distortion of calculation results caused by the reliance on external benchmarks in traditional methods. It constructs a virtual benchmark system by identifying stable points of measuring points inside the cross section, thus eliminating the dependence on external control points. At the same time, it integrates the rigid body fitting method with minimum spatial distance constraints, effectively removing the non-real rigid body deformation of the entire cross section, suppressing geometric distortion caused by proportional drift and shear deviation, accurately extracting the local real deformation displacement of the tunnel structure, and significantly improving the accuracy of the crown settlement calculation.

[0033] This invention achieves precise selection of stable points through quantitative stable point scoring and shape preservation indices, and, combined with stable point anti-shake processing, improves the stability of the virtual reference system and the continuity of the settlement calculation sequence. Addressing the common problem of missing measurement points during construction, a missing measurement tolerance and data reinjection mechanism is designed to avoid interruptions in the calculation sequence and abrupt changes in results, ensuring the continuity and traceability of settlement calculations. The output of settlement data in both the Z-axis and normal directions enables cross-validation of settlement results, further enhancing the reliability of the calculation results.

[0034] The early warning method provided by this invention is deeply coupled with the settlement calculation method. Based on the actual settlement calculation results, it quantifies the fluctuation of settlement data through a sliding window, constructs an adaptive early warning threshold with single point and linkage, and superimposes the CUSUM test and short-term prediction extrapolation trend criteria to realize the graded early warning of tunnel arch settlement risk. It solves the problems of fixed threshold and easy false alarm and missed alarm in traditional early warning methods, and improves the reliability and pertinence of early warning. Attached Figure Description

[0035] Figure 1 This is a flowchart of the tunnel arch settlement calculation method based on the minimum distance constraint of coupled space according to the present invention.

[0036] Figure 2 This is a schematic diagram of the tunnel cross-section observation points and three-dimensional coordinate system of the present invention, wherein the X-axis is the arch direction, the Y-axis is the tunnel axis, the Z-axis is the vertical direction, and the measuring points include the arch apex No. 1, the left and right middle layers No. 2 / 3, and the left and right lower layers No. 4 / 5.

[0037] Figure 3 This is a schematic diagram of the minimum spatial distance constraint of the present invention.

[0038] Figure 4 This is a flowchart of the tunnel arch settlement early warning method of the present invention. Detailed Implementation

[0039] Example 1: As Figure 1 As shown in the figure, this embodiment is a method for calculating the settlement of the tunnel arch with coupled spatial minimum distance constraints. The specific steps include:

[0040] S100. Five observation points are set up on the same cross section of the tunnel, including the arch apex, left and right middle layer points, and left and right lower layer points, to obtain the relative three-dimensional coordinates of each observation point under multiple observation periods.

[0041] In this embodiment, a right-handed three-dimensional coordinate system is defined: the X-axis represents the tunnel arch direction (lateral), the Y-axis represents the tunnel axis (longitudinal), and the Z-axis is vertical with upward being positive; five observation points are set up on the same cross-section of the tunnel, such as... Figure 2 As shown, the top of the arch (point 1), the middle left layer (point 2), the middle right layer (point 3), the lower left layer (point 4), and the lower right layer (point 5) were measured using a total station to collect the relative three-dimensional coordinates of each measuring point over multiple periods.

[0042] The relative three-dimensional coordinates of five measuring points on the same cross-section under multiple observation periods: ; Where i∈{1,2,3,4,5} is the measurement point number, and k is the observation period number.

[0043] S200. Taking the first observation as the reference period k0, set a stable point candidate set C containing all observation points except the crown apex (C={2, 3, 4, 5}, excluding crown apex point 1 to avoid absorbing actual settlement). For any observation period k after the reference period k0, on the candidate set C, calculate the stable point score of each point in the candidate set by quantifying the change in the Euclidean distance between the point pairs containing the points to be scored relative to the reference period k0, and select the 3 points with the smallest scores to form the current stable point set.

[0044] In this embodiment, for a candidate point u∈C, using the reference period k0 as a benchmark, the change in distance between u and other candidate points in each period is calculated, and then the stability score of point u is calculated. ; ; Where u and v are points in the candidate set, and C is the stable point candidate set. , Let u and v be the three-dimensional coordinates of point k during the observation period. , The reference period is defined by the three-dimensional coordinates of points u and v at point k0.

[0045] When calculating score(u), Huber loss or M-estimation can be used to weight large deviations to reduce the impact of gross errors or local outliers on the selection of stable points.

[0046] In this embodiment, if there are tied scores, multiple candidate triplets of stable points are formed. The shape preservation index of each candidate triplet is calculated by quantifying the change of each point in the triplet relative to the Euclidean distance relative to the reference period k0. The triplet with the smallest index is selected as the final stable point set. ; in, J is the shape preservation index of candidate triple S during the observation period k. S The smaller (k) is, the closer the geometry of the stable point set is to the reference period, and the better the stability; S is the candidate triplet for stable points; ω ij For point-to-point weights, ω can be taken when there is no prior knowledge. ij =1 If the ranging accuracy or geometric conditions are known, then weights can be assigned inversely proportional to the accuracy. , Let i and j be the three-dimensional coordinates of points i and j during the observation period k. , Let i and j be the three-dimensional coordinates of points i and j in the reference period k0.

[0047] In this embodiment, the preset improvement rate is set to 10%, if the current shape retention index If the improvement in the stable point registration residual RMS compared to the previous period is less than 10%, then the stable point set from the previous period will be used directly to avoid fluctuations in the calculation results caused by frequent switching of the stable point set.

[0048] S300. Based on the current stable point set, construct an objective function that integrates the stable point registration residual and the minimum spatial distance constraint, and solve for the rigid body parameters of the observation period k, including the rotation matrix R. k Translation vector t k The rigid body parameters are used to calculate the derigid displacement of all observation points on the cross section.

[0049] In this embodiment, the stable point set is not only used for rigid body registration, but also needs to ensure that the geometric relationship between point pairs remains unchanged, i.e., "spatial minimum distance constraint". Figure 3 As shown, specifically, it is required that the distance difference between the stable point pair (i, j) and the reference period be as small as possible in any observation period, so as to suppress geometric distortion caused by scaling drift and shear deviation during the overall rigid body registration process; and to ensure that the virtual reference system formed by the stable points remains rigid throughout multi-period calculations. The degree of violation of the minimum spatial distance constraint is determined by J. S (k) is characterized and output as a quality control indicator along with the registration residual RMS.

[0050] In each observation period k, the set of stable points S for that period has been determined. In order to eliminate the influence of the overall rigid body motion of the cross-section, it is necessary to align the set of points for the observation period to the reference period k0 and solve for the rigid body parameters: ;

[0051] The objective function is defined as: ; Where, ω i α represents the stability point weight; α represents the spatial minimum distance constraint strength; S represents the current stability point set. Let i be the three-dimensional coordinates of point i during the observation period k. J represents the three-dimensional coordinates of point i at reference period k0; S (k) is the shape preservation index of the stable point set, and is the quantization term of the minimum spatial distance constraint; rigid body parameters include the rotation matrix R. k Translation vector t k .

[0052] S310, Calculate the stable point set During the observation period weighted center of mass The weighted centroid of reference period k0 ; ; S320, based on stable point sets During the observation period The stable coordinates and weighted centroids of the reference period k0 are used to construct the covariance matrix. ; ;

[0053] S330. Perform singular value decomposition on the covariance matrix to obtain... Thus, the initial rotation matrix is ​​obtained. ,like Then, the sign of the last column of V is corrected to ensure the orthogonality of the rotation matrix, and the initial translation vector is calculated based on the initial rotation matrix. ; ;

[0054] S340, Based on initial rigid body parameters ( , The objective function is iteratively optimized using the iterative reweighted least squares method, the stationary weights are updated, and the shape preservation index is linearized. The rotation matrix R is alternately minimized and updated. k Translation vector t k Continue until the convergence criterion is met, and the final rigid body parameters are obtained.

[0055] The convergence criterion in this embodiment includes: Rotation increment: ; Translation increment ; in, , Let n be the rotation matrix and translation vector for the nth iteration. , Let be the rotation matrix and translation vector for the (n-1)th iteration.

[0056] S350, after obtaining the final rigid body parameters (R) k , tk After that, calculate the rigid body displacement for all observation points i∈{1,2,3,4,5} on the cross section: ; in, Let i be the derigid displacement of point i at time k during the optical measurement period.

[0057] S400. Based on the arch fitting of the reference section, the local unit normal vector of each observation point is obtained. The rigid body displacement is projected onto the Z-axis direction and the normal direction respectively, and the Z-direction settlement and normal settlement of each observation point are obtained respectively.

[0058] Settlement is primarily determined by changes in the vertical coordinate, with "downward being positive." This is in contrast to rigid body displacement. Z-axis settlement is defined as: ;

[0059] That is, the projection of the rigid body displacement onto the Z-axis is taken, where e Z =(0,0,1) ⊤ is the unit basis vector of the Z-axis.

[0060] For the arch apex (point 1), the Z-direction settlement is approximately the same as the normal settlement and can be directly used as the settlement amount; for the waist points (points 2-5), the Z-direction settlement mainly reflects the vertical downward sinking effect, but it is not sensitive enough to the inward movement of the arch waist.

[0061] To more accurately reflect the "inward convergence" behavior of the arch waist, the normal direction needs to be defined based on the arch fitting. During the reference period k0, a circular arc or quadratic curve z=f(x) is fitted using the distribution of each observation point in the X–Z plane, and the tangent slope f′(x) is calculated at point i. i The reference period unit normal vector of point i is defined as: ; The normal direction points towards the arch / cave interior.

[0062] Normal settlement is the projection of rigid body displacement onto the normal direction. ; For the arch apex (point 1), since its tangent is approximately horizontal, n1≈(0,0,−1), which is basically consistent with the Z direction; for the waist points (points 2~5), there is an angle between the normal and the vertical, and the normal settlement is more sensitive to the inward convergence of the arch waist.

[0063] This embodiment outputs data in parallel for each measuring point. and , representing vertical settlement and normal settlement respectively. Arch apex: The results of the two diameters should be basically consistent for cross-verification; Waist point: The difference between the two diameters reflects the degree of inward displacement of the arch waist, which can help determine the convergence trend of the structure.

[0064] During tunnel construction, some monitoring points may be missed during certain observation periods due to obstruction, equipment failure, or abnormal data transmission. If too many points are missing, it can prevent the formation of effective stable point combinations and even interrupt the settlement sequence. To ensure the continuity and availability of monitoring results, this embodiment incorporates a fault-tolerance and recharge mechanism.

[0065] When the number of valid points in the candidate stable point set {2,3,4,5} is less than 3, a stable point triangle cannot be directly formed. In this case, the system automatically uses the minimum solvable subset. If only one point is missing (i.e., 3 points remain usable), a stable point set can still be formed, and the solution can be directly obtained. If only 2 points remain, a weak solution with historical constraints is introduced, and the solution is compared with the solution obtained in the previous period (R... k−1 ,t k−1 Perform joint constraints to estimate the results for this period; if only 1 point remains or all points are missing, stop the calculation and record "Missing Period" in the output.

[0066] When missing data points are observed again in subsequent periods, their weights need to be gradually restored to avoid abrupt changes in results: In the first period after the missing data points are restored, a weight of 0.5 is assigned; in the second period, it is increased to 0.8; and in the third period, it is restored to 1.0. This is the "2-3 period gradual reinjection" method, ensuring a smooth transition and avoiding discontinuities in the sequence. The reinjection only affects the restored data points themselves and does not affect the stable calculation of other data points.

[0067] Example 2: This example is a tunnel arch settlement calculation device with coupled spatial minimum distance constraints, specifically including: The data management module is used to set up at least five observation points on the same cross section of the tunnel, including the top of the arch, the left and right middle layer points, and the left and right lower layer points, and to obtain the relative three-dimensional coordinates of each observation point under multiple observation periods; The stable point identification module is used to set the stable point candidate set to include all observation points except the apex of the arch. For any observation period k after the reference period k0, the stable point score of each point in the candidate set is calculated by quantifying the change in the Euclidean distance between the point pairs containing the points to be scored relative to the reference period k0. The three points with the smallest scores are selected to form the stable point set for the current period. The rigid body fitting module is used to construct an objective function that integrates the registration residuals of stable points and the minimum spatial distance constraint based on the current stable point set, solve for the rigid body parameters of the observation period k, and use the rigid body parameters to calculate the de-rigid body displacement of all observation points of the section. The settlement extraction module is used to obtain the local unit normal vector of each observation point based on the arch fitting of the cross section during the reference period, and to project the rigid body displacement onto the Z-axis direction and the normal direction respectively, so as to obtain the Z-axis settlement and normal settlement of each observation point respectively.

[0068] Example 3: This example is a storage medium that stores a computer program that can be executed by a processor. When the computer program is executed, it implements the steps of the tunnel arch settlement calculation method described in Example 1.

[0069] Example 4: This example is a tunnel arch settlement calculation device, which has a memory and a processor. The memory stores a computer program that can be executed by the processor. When the computer program is executed, it implements the steps of the tunnel arch settlement calculation method described in Example 1.

[0070] Example 5: Figure 4 As shown, this embodiment is a method for early warning of tunnel arch settlement, which specifically includes the following steps: I. Based on the tunnel arch settlement calculation method described in Example 1, the Z-axis settlement and normal settlement of each observation point on the same cross section of the tunnel under multiple observation periods are calculated.

[0071] II. Set a sliding window, and within the sliding window, calculate the standard deviation of the settlement sequence increment for each observation point. The settlement sequence is a sequence composed of the Z-axis settlement or normal settlement of each observation point in multiple periods within the sliding window.

[0072] In this embodiment, for each measuring point i, the standard deviation of the settlement sequence increment is calculated within a window W (generally 5 to 10 periods): ; in, Let W be the standard deviation of the settlement sequence at the i-th observation point; W be the sliding window; |W| be the number of observation periods within the sliding window; The settlement of measuring point i during the observation period k within the sliding window; Let be the average settlement of measurement point i within the sliding window.

[0073] III. Based on the standard deviation of the settlement sequence increments at each observation point, construct the single-point early warning threshold for each observation point and the linkage early warning threshold for adjacent observation points.

[0074] In this embodiment, the standard deviation σ is used. i Define an adaptive threshold: Single-point threshold: ; Where c is a coefficient (preferably 1.96 to 2.58), when At that time, it was judged as exceeding the limit.

[0075] Linkage threshold: Define linkage criteria for adjacent points i and j. ; If the settlement difference between the two points This indicates a local abnormality; in, Let be the single-point early warning threshold for the i-th observation point; is the linkage warning threshold between observation point i and observation point j; c is the threshold coefficient; , denoted as the standard deviations of the settlement sequences at observation points i and j, respectively.

[0076] IV. Combining the Z-axis settlement, normal settlement, and adaptive early warning threshold with the settlement trend criteria, a graded early warning judgment is made on the settlement risk of the tunnel arch.

[0077] In this embodiment, the settlement trend criteria include: CUSUM test and short-term prediction extrapolation. The CUSUM test is used to capture the offset of the cumulative sum of settlement increments. The short-term prediction extrapolation includes using an autoregressive model AR(1) or Kalman filter to make short-term predictions on the settlement sequence. If the measured value is consistently higher than the upper limit of the prediction interval, a trend warning is triggered.

[0078] In this embodiment, multiple warning levels are set by combining the degree of exceeding limits with trend characteristics: (1) Level I (Attention) Condition: The single point or linkage indicator exceeds 1.0T but is less than 1.5T.

[0079] Action taken: Mark and track the item, but do not trigger an alarm for now.

[0080] (2) Level II (Warning) Conditions: Exceeding 1.5T, or approaching the threshold for 2-3 consecutive periods, and the trend criterion shows an upward trend.

[0081] Action taken: An early warning has been triggered. It is recommended to review the observations.

[0082] (3) Level III (Alarm) Condition: Exceeding 2.0T, and accompanied by a continuous trend of deterioration.

[0083] Action: Immediately trigger the alarm and notify the construction and supervision teams to take safety measures.

[0084] The following are some specific examples to illustrate this:

[0085] Example 1 (FHDL0+780 section of a safety monitoring project) (1) Operating conditions Five observation points were set up at the tunnel cross-section FHDL0+780: the arch apex (1), the left and right middle-level points (2 and 3), and the left and right lower-level points (4 and 5). Using the first period k0 as the reference period, the relative coordinates of the five points were obtained in meters each period using a total station.

[0086] (2) Sample data The table below provides observation data for three periods, with the first period serving as a reference period:

[0087] (3) Processing procedure 1. Stable Point Identification Candidate set: {2,3,4,5}; Each period calculates score(u), and selects 3 points as the stable point set S. In the example, points 2, 3, and 5 are selected as stable points.

[0088] 2. Rigid body fitting Weighted SVD initialization was used, followed by IRLS iterative convergence; Output stable point RMS < 0.5mm, shape retention index J S (k) < 1.0 mm², which meets the stability requirements.

[0089] 3. Remove rigid body displacement The displacement after removing the rigid body is obtained by calculating the displacement at five points.

[0090] 4. Sedimentation Extraction For the apex of the arch (number 1), the calculation yields: ①Z-axis settlement: Phase 2 = 3.8mm, settlement; Phase 3 = 8.1mm, settlement; ②Normal settlement: approximately consistent with Z-axis settlement.

[0091] For the waist points (points 2, 3, and 5), the results show that the normal settlement is slightly greater than the Z-axis settlement, indicating a slight inward displacement of the arch waist.

[0092] (4) Results and Interpretation The settlement curve of the arch apex showed continuous sinking within three phases, with the settlement rate increasing in each phase, which is consistent with the pattern under the influence of blasting construction at the tunnel face.

[0093] The normal settlement at the waist point accumulated to about 2-3 mm within 3 phases, which is slightly greater than the vertical settlement, indicating that the arched waist has an inward convergence trend.

[0094] Based on the adaptive threshold, the apex of the arch triggered Level I attention in Phase 3, but did not trigger Level II / III warnings.

[0095] (5) Output illustration Settlement curves of parallel diameters (Z-axis and normal direction); RMS and J S The time series curve of (k); Warning Log: Phase 3, Point 1 triggered Level I attention, type = single point threshold exceeded.

[0096] Example 2 (Missing Test Tolerance) (1) Operating conditions In the fourth phase of observations at tunnel section FHDL0+780, point 4 could not be observed with valid coordinates due to obstruction by the station, resulting in a single-point missing measurement. Only three points (points 2, 3, 4, 5) are available in the candidate set {2, 3, 4, 5}.

[0097] (2) Sample data The observation period is k=4, and the input data is as follows (unit: m):

[0098] (3) Processing procedure 1. Stable Point Identification The valid candidate set points are {2,3,5}, which exactly satisfies the 3 conditions. After the stability score was calculated, points 2, 3, and 5 were selected as the stability set S.

[0099] 2. Rigid body fitting The rigid body parameters (R4, t4) are solved based on the stable point set, and the results converge and are stable. RMS=0.6mm, J S (4) = 1.2 mm 2 It is slightly higher than in the previous period, but still within an acceptable range.

[0100] 3. Handling of missing measurement points No settlement results were output for point 4 due to missing measurements. The output report was marked "Missing Measurement Tolerance" and the reason for the missing measurement was recorded.

[0101] (4) Results and Interpretation The Z-axis settlement of the apex of the arch (No. 1) in the fourth phase was 13.0 mm, continuing to sink compared to the third phase; The normal settlements at the waist points (points 2, 3, and 5) were approximately 5.0 mm, 5.3 mm, and 4.8 mm, respectively, showing good continuity. The missing measurement at point 4 did not affect the overall solution, and the system successfully completed the fitting through the "minimum solvable subset".

[0102] (5) Restoration and Refilling During the fifth phase of observation, point 4 resumed normal measurement. The system assigns it a weight of 0.5, and gradually restores it to 1.0 in the 6th period; The report records the process of "Recovery of missing data at point 4 → Weight reinjection".

[0103] (6) Output illustration In the settlement curve, point 4 shows a null value in the 4th period, and gradually recovers in the 5th and 6th periods; The warning log indicates: Missing measurement point for phase 4 = number 4, handling method = minimum solvable subset; RMS and J SThe (k) curve showed a slight increase in period 4, but did not trigger an alert.

[0104] Example 3 (Batch Processing Alerts) (1) Operating conditions During the construction of a certain tunnel, monitoring personnel used a total station to conduct manual periodic measurements of the cross-section observation points once a day, and imported the measurement results into the software system corresponding to this method for batch processing and calculation.

[0105] (2) Monitoring settings Observation period: 1 day / period; Sliding window: W=6 (approximately 6 days); Threshold coefficient: c=2.0, corresponding to a 95% confidence level; Early warning mechanism: adaptive threshold + trend criteria (CUSUM / short-term extrapolation).

[0106] (3) Sample data The normal settlement results of the apex of the arch over six consecutive periods are as follows (unit: mm):

[0107] (4) Processing procedure After each measurement data is imported into the system, it automatically completes the identification of stable points, rigid body fitting, and calculation of displacement after rigid body removal. The system calculates the settlement value at each point and obtains the threshold based on the sliding window statistics; When the settlement of the arch apex exceeds 2.0T and the trend continues to rise, the system determines it to be a Level III alarm.

[0108] (5) Results and Interpretation The settlement at the top of the arch continued to exceed the limit from the 12th period onwards, and was accompanied by a trend of increasing, triggering a Level III alarm; The settlement at the waist level did not exceed the threshold and no warning was triggered. The system output includes settlement curves, CUSUM trend curves, and early warning logs.

[0109] (6) Explanation This method can be applied to both real-time data streams and batch processing scenarios following manual periodic measurements. For cross-sectional coordinate data acquired by a total station, the early warning function can be achieved through manual periodic measurements and batch processing, ensuring the feasibility of the method under actual construction conditions.

Claims

1. A method for calculating tunnel arch settlement with coupled spatial minimum distance constraints, characterized in that, include: S100. Set up at least five observation points on the same cross section of the tunnel, including the top of the arch, the left and right middle layer points and the left and right lower layer points, and obtain the relative three-dimensional coordinates of each observation point under multiple observation periods. S200. Set the candidate set of stable points to include all observation points except the apex of the arch. For any observation period k after the reference period k0, calculate the stable point score of each point in the candidate set by quantifying the change in the Euclidean distance between the point pairs containing the points to be scored relative to the reference period k0. Select the three points with the smallest scores to form the stable point set for the current period. S300. Based on the current stable point set, construct an objective function that integrates the stable point registration residual and the minimum spatial distance constraint, solve for the rigid body parameters of the observation period k, and use the rigid body parameters to calculate the de-rigid body displacement of all observation points of the section. S400. Based on the arch fitting of the reference section, the local unit normal vector of each observation point is obtained. The rigid body displacement is projected onto the Z-axis direction and the normal direction respectively, and the Z-direction settlement and normal settlement of each observation point are obtained respectively.

2. The method for calculating tunnel arch settlement with minimum distance constraint in coupled space according to claim 1, characterized in that, The calculation of the stable point score for each point in the candidate set by quantifying the change in the Euclidean distance between point pairs containing the points to be scored relative to the reference period k0 includes: ； Where u and v are points in the candidate set, and C is the stable point candidate set. , Let u and v be the three-dimensional coordinates of point k during the observation period. , The reference period is defined by the three-dimensional coordinates of points u and v at point k0.

3. The method for calculating tunnel arch settlement with minimum distance constraint in coupled space according to claim 1, characterized in that, The selection of the three points with the lowest scores to form the current stable point set includes: If there are ties in the scores, multiple candidate triplets for stable points are formed. The shape preservation index of each candidate triplet is calculated by quantifying the change of each point in the triplet with respect to the Euclidean distance relative to the reference period k0. The triplet with the smallest index is selected as the final stable point set.

4. The method for calculating tunnel arch settlement with minimum distance constraint in coupled space according to claim 3, characterized in that, The method of calculating the shape preservation index of each candidate triplet by quantifying the change in Euclidean distance of each point in the triplet relative to the reference period k0 includes: ； in, ω is the shape preservation index of candidate triple S at observation period k; S is the stable candidate triple; ij Point-to-point weights; , Let i and j be the three-dimensional coordinates of points i and j during the observation period k. , Let i and j be the three-dimensional coordinates of points i and j in the reference period k0.

5. The method for calculating tunnel arch settlement under minimum distance constraint in coupled space according to claim 1, characterized in that, Step S200 includes: If the improvement of the current period's shape retention index or stable point registration residual compared to the previous period is less than the preset value, then the stable point set of the previous period will be used directly.

6. The method for calculating tunnel arch settlement under minimum distance constraint in coupled space according to claim 1, characterized in that, The objective function constructed based on the current stable point set, which integrates the stable point registration residual and the spatial minimum distance constraint, includes: ； Where, ω i α represents the stability point weight; α represents the spatial minimum distance constraint strength; S represents the current stability point set. Let i be the three-dimensional coordinates of point i during the observation period k. J represents the three-dimensional coordinates of point i at reference period k0; S (k) is the shape preservation index of the stable point set, and is the quantization term of the minimum spatial distance constraint; rigid body parameters include the rotation matrix R. k Translation vector t k .

7. The method for calculating tunnel arch settlement with minimum distance constraint in coupled space according to claim 1, characterized in that, The solution yields the rigid body parameters for the observation period k, including: First, calculate the stable point set. During the observation period The weighted centroid of the reference period k0 and the weighted centroid of the reference period k0; Based on stable point set During the observation period The stable coordinates and weighted centroids of the reference period k0 are used to construct the covariance matrix; Singular value decomposition is performed on the covariance matrix to obtain the initial rotation matrix, and the initial translation vector is then calculated based on the initial rotation matrix. Based on the initial rigid body parameters, the objective function is iteratively optimized using the iterative reweighted least squares method. The stable point weights are updated and the shape preservation index is linearized. The rotation matrix and translation vector are alternately minimized and updated until the convergence criterion is met, and the final rigid body parameters are obtained.

8. The method for calculating tunnel arch settlement under minimum distance constraint in coupled space according to claim 1, characterized in that, It also includes steps for handling missing test errors: When the number of valid observation points in the candidate stable point set is less than 3, if there are 3 valid points remaining, the solution is performed directly using these 3 points as the stable point set; if there are 2 valid points remaining, the rigid body parameters from the previous period are introduced as historical constraints for joint solution; if the number of valid points remaining is ≤1, the current solution is terminated and the missing measurement information is recorded.

9. The method for calculating tunnel arch settlement with minimum distance constraint in coupled space according to claim 8, characterized in that, It also includes the data backfeeding step: When a missing observation point is restored to observation, it is assigned a weight of 0.5 in the first period after restoration, the weight is increased to 0.8 in the second period, and the weight is restored to 1.0 in the third period; the weight adjustment is only made for the restored point itself.

10. A tunnel arch settlement calculation device with coupled spatial minimum distance constraints, characterized in that, include: The data management module is used to set up at least five observation points on the same cross section of the tunnel, including the top of the arch, the left and right middle layer points, and the left and right lower layer points, and to obtain the relative three-dimensional coordinates of each observation point under multiple observation periods; The stable point identification module is used to set the stable point candidate set to include all observation points except the apex of the arch. For any observation period k after the reference period k0, the stable point score of each point in the candidate set is calculated by quantifying the change in the Euclidean distance between the point pairs containing the points to be scored relative to the reference period k0. The three points with the smallest scores are selected to form the stable point set for the current period. The rigid body fitting module is used to construct an objective function that integrates the registration residuals of stable points and the minimum spatial distance constraint based on the current stable point set, solve for the rigid body parameters of the observation period k, and use the rigid body parameters to calculate the de-rigid body displacement of all observation points of the section. The settlement extraction module is used to obtain the local unit normal vector of each observation point based on the arch fitting of the cross section during the reference period, and to project the rigid body displacement onto the Z-axis direction and the normal direction respectively, so as to obtain the Z-axis settlement and normal settlement of each observation point respectively.

11. A storage medium having a computer program stored thereon that can be executed by a processor, characterized in that, When the computer program is executed, it implements the steps of the tunnel arch settlement calculation method according to any one of claims 1 to 9.

12. A tunnel arch settlement calculation device, comprising a memory and a processor, wherein the memory stores a computer program executable by the processor, characterized in that, When the computer program is executed, it implements the steps of the tunnel arch settlement calculation method according to any one of claims 1 to 9.

13. A method for early warning of tunnel arch settlement, characterized in that, include: Based on the tunnel arch settlement calculation method according to any one of claims 1 to 9, the Z-direction settlement and normal settlement of each observation point on the same cross section of the tunnel under multiple observation periods are calculated; Set a sliding window, and within the sliding window, calculate the standard deviation of the settlement sequence increment for each observation point. The settlement sequence is a sequence composed of the Z-axis settlement or normal settlement of each observation point in multiple periods within the sliding window. Based on the standard deviation of the settlement sequence increment at each observation point, a single-point early warning threshold and a linkage early warning threshold between adjacent observation points are constructed for each observation point. By combining the Z-axis settlement, normal settlement, and adaptive early warning threshold, and overlaying settlement trend criteria, a graded early warning judgment is made on the settlement risk of the tunnel arch.

14. The tunnel arch settlement early warning method according to claim 13, characterized in that, The calculation of the standard deviation of the settlement sequence increment at each observation point includes: ； in, Let W be the standard deviation of the settlement sequence at the i-th observation point; W be the sliding window; |W| be the number of observation periods within the sliding window; The settlement of measuring point i during the observation period k within the sliding window; Let be the average settlement of measurement point i within the sliding window.

15. The tunnel arch settlement early warning method according to claim 13, characterized in that, The calculation formula for the single-point early warning threshold includes: ； The formula for calculating the linkage early warning threshold is: ； in, Let be the single-point early warning threshold for the i-th observation point; is the linkage warning threshold between observation point i and observation point j; c is the threshold coefficient; , denoted as the standard deviations of the settlement sequences at observation points i and j, respectively.

16. The tunnel arch settlement early warning method according to claim 13, characterized in that, The settlement trend criteria include: CUSUM test and short-term prediction extrapolation, wherein the CUSUM test is used to capture the offset of the cumulative sum of settlement increments, and the short-term prediction extrapolation includes using an autoregressive model AR(1) or Kalman filter to make short-term predictions on the settlement sequence.

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