A tunnel vault settlement surveying and mapping result three-dimensional reconstruction analysis method

Abstract

The application discloses a tunnel vault subsidence mapping result three-dimensional reconstruction analysis method, and relates to the technical field of tunnel deformation monitoring. Two-period point records of at least two point cloud sources are acquired and converted to a unified tunnel coordinate system, and a lining surface unit graph is established and frozen. Two-period point records are distributed according to adjacent edge mutual exclusion, forming edge relative displacement increments and uncertainties. A limited multi-scale closed loop is generated to determine abnormal loops by normalizing the closed residual error, and a modified edge set is obtained and rechecked to form a compatible subgraph. Connected components are reconstructed according to the remaining edges, and are marked as absolute effective, only relative and unverified states respectively after common quality inspection. Three-dimensional displacement, the modified edge set, closed loop uncovered areas, connected component states and supplementary survey areas are output. The application can improve the spatial compatibility, state interpretability and supplementary survey traceability of multi-source point cloud deformation results.

Description

Technical Field

[0001] This invention relates to the field of tunnel three-dimensional deformation monitoring technology, and in particular to a three-dimensional reconstruction and analysis method for tunnel arch settlement mapping results. Background Technology

[0002] Traditional 3D tunnel deformation monitoring typically involves coordinate registration, surface fitting, and geometric difference calculation of point clouds collected at different times, followed by local smoothing or global optimization to generate continuous deformation results. This approach often relies on registration convergence, local fitting residuals, or surface differences as criteria for data quality and deformation assessment, lacking sufficient verification of whether dispersed measurement results can collectively represent continuous and consistent tunnel surface displacement. Tunnel surfaces exhibit repetitive geometry, occlusion, and local measurement gaps. Even small local residuals across different periods may still contain positional mismatches. Corresponding errors, after global fitting or smoothing propagation, can easily manifest as continuous spurious deformation, affecting the accuracy and interpretability of the monitoring results.

[0003] Multi-source point clouds originate from different acquisition locations and observation conditions, exhibiting differences in coordinate reference, sampling density, noise level, and coverage. Traditional fusion processing typically involves first performing overall registration of all sources, then directly stitching, averaging, or weighting in overlapping areas, and may reuse nearby point records within overlapping local neighborhoods to establish inter-period correlations. The similarity of tunnel lining surfaces along the axial and circumferential directions introduces ambiguity into local correlations. Occlusion, changes in viewing angle, and local missing measurements further alter the spatial distribution of available points, leading to interdependent estimation errors in adjacent areas. Real local deformation, inter-source coordinate deviations, and inter-period mismatches may be simultaneously absorbed into the same fitting result, making it difficult to distinguish different physical causes and easily resulting in distortions in displacement direction, range, and continuity.

[0004] Traditional back-end processing typically makes anomaly judgments based on single cross-sections, single local regions, or overall statistical indicators, and then directly uses the smoothed displacement field for state output. There is a lack of cross-verification between local judgments that reflects the spatial continuity of the tunnel surface; the correspondence between the source of anomalies and affected measurements is unclear; local anomalies may be diluted by surrounding data or spread to adjacent areas. When data sources are insufficient, local solutions are unstable, observation coverage is incomplete, or absolute references are missing, unreliable results can easily be confused with no obvious deformation. The applicable boundaries of absolute displacement and relative change are not easily defined, leading to misjudgments, missed judgments, and feedback lags. Furthermore, subsequent re-measurements lack traceable positioning evidence, reducing the reliability of the monitoring system. Summary of the Invention

[0005] To address the shortcomings of existing technologies, this invention provides a three-dimensional reconstruction and analysis method for tunnel arch settlement survey results.

[0006] To achieve the above objectives, this invention provides a three-dimensional reconstruction and analysis method for tunnel arch settlement survey results, the technical solution of which is as follows: Obtain reference period records and monitoring period records from at least two point cloud sources, and convert them to a unified tunnel coordinate system based on the source identifier, period identifier, and coordinate transformation relationship; Based on the reference period record, establish a circumferentially partitioned and circumferentially closed lining surface element diagram, and freeze the element representative position, edge specification direction and edge orthogonal basis; The two-phase point evidence is allocated according to the mutual exclusion of adjacent edges on the surface, and the relative displacement increment and uncertainty of the edge are formed based on the local inter-phase transformation of the two-end point evidence of each edge. In the lining surface unit diagram, a finite axial, circumferential and axial-circumferential hybrid multi-scale closed loop is generated. The relative displacement increment of the edge in each closed loop is directly converted to the corresponding closed loop root. The closed residual is accumulated according to the edge direction to form a closed residual. The closed residual is normalized according to the propagation uncertainty to determine the abnormal loop. Based on the participation relationship between abnormal cycles and modifiable edges and the modification cost, the set of modified edges that hit each abnormal cycle and have the minimum total cost is obtained. Only after proving that the set of modified edges is optimal are the corresponding edges isolated and the closed cycle is re-examined to form a compatible subgraph. Reconstruct each connected component based on the relative displacement increment of the remaining edges of the compatible subgraph. When the reconstructed relation is full rank, the condition number is qualified, and the solution is finite, the connected component with valid and consistent independent displacement anchor constraints is marked as an absolutely valid state, the connected component that originally did not have independent displacement anchor constraints and was subject to zero mean constraints is marked as a relative state only, and the remaining connected components are marked as unverified states. Outputs 3D displacement, modified edge set, closed-loop uncovered area, connected component status, and supplementary measurement area.

[0007] In summary, the present invention has at least one of the following beneficial technical effects: 1. This invention organizes the coordinate conversion of multi-source reference period point records and monitoring period point records, the freezing of the reference period lining surface unit diagram, the mutually exclusive allocation of point evidence, the local inter-period estimation of edge tail and edge head, and the source consistency fusion into a continuous processing chain. Coordinate unification can only make different sources have comparable positions, but cannot eliminate inter-period mismatch caused by repeated tunnel geometry; using local fitting alone can only reflect local residuals, and it is difficult to reveal the adjacent estimation dependence caused by point record reuse; simply aggregating multi-source results cannot automatically eliminate conflicting sources. By first fixing the surface unit identity, representative position, and edge orthogonal basis, and then making the point record support only one adjacent surface edge, and applying the local intertemporal transformations of the edge tail and edge head from each source to the corresponding representative position and then subtracting them in the same edge orthogonal basis, the local transformation can be transformed into a source edge relative displacement increment with a clear physical object and auditable evidence between edges. Continuing to use source uncertainty to screen consistent sources and perform information fusion, an edge relative displacement increment carrying uncertainty is formed, making it difficult for coordinate differences, local mismatches, and source conflicts to be directly incorporated into the continuous deformation results. Furthermore, the point record allocation relationship, source subset, and fusion uncertainty can be used for verification, providing mutually independent, directionally consistent, and traceable intermediate data for subsequent spatial compatibility judgment.

[0008] 2. This invention uses the aforementioned relative displacement increments and uncertainties of the edges as continuous inputs. Within a frozen finite multi-scale closed loop, each edge quantity is directly converted to the closed loop foundation and accumulated directionally. By propagating uncertainty and normalizing the closure residuals, edge quantities that only have local fitting basis are transformed into spatially compatible evidence capable of verifying whether multiple adjacent regions can be explained by the same continuous displacement field. Closed loop anomalies can only indicate incompatible relationships but cannot individually determine the edges to be processed. Directly deleting edges with large local residuals may disrupt normal closed loops. Therefore, based on the participation relationships of the anomaly loop and the cost of evidence, a set of modified edges proven to be optimal is obtained. After isolation, a complete closed loop is regenerated for re-examination, ensuring that the retained edges are subject to the joint constraints of anomaly and normal evidence. Reconstructing 3D displacement only on the compatible sub-map after re-inspection, and forming absolutely valid state, relative state only, and unverified state according to independent displacement anchor points, zero mean specification, and solution validity, and limiting the corresponding output, can avoid interpreting insufficient data, topology non-coverage, or solution failure as zero deformation or a definite alarm. Then, the isolated area, non-covered area, and unverified component are passed as supplementary measurement objects and the processed version is retained, forming a traceable closed loop from compatibility verification, state determination to feedback update, which helps to suppress the propagation of mismatch error and improve the reliability of tunnel 3D deformation judgment. Attached Figure Description

[0009] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0010] Figure 1 This is a flowchart of a three-dimensional reconstruction and analysis method for tunnel arch settlement survey results provided in an embodiment of the present invention.

[0011] Figure 2 This invention relates to the frozen tunnel surface unit diagram and the multi-scale closed-loop spatial organization diagram.

[0012] Figure 3 This is the correspondence between the two phases of exclusive point evidence and the local transformation diagram at the edge of the present invention.

[0013] Figure 4 This invention relates to a matrix graph involving abnormal loops and modifiable edges.

[0014] Figure 5 This is the connectivity component reliability state and supplementary test version transition diagram of the present invention. Detailed Implementation

[0015] The present invention will be further described below with reference to the accompanying drawings and specific embodiments. It should be understood that the embodiments described are for illustrative purposes only and are not intended to limit the scope of protection of the present invention.

[0016] Example This invention is applicable to a three-dimensional deformation monitoring system that periodically collects data from at least two point cloud sources on the tunnel lining surface. In situations where there is obstruction, differences in point density, and inconsistencies in local correspondence quality along the tunnel route, directly stitching together all point records and then performing point-by-point differencing can easily lead to local conflicts and minor erroneous correspondences between sources propagating to the global displacement results, and potentially misclassifying areas not covered by the closed loop as having no deformation. This embodiment freezes the surface map for the reference period, assigns point evidence from the two periods according to mutually exclusive adjacent edges, first forming independent edge relative displacement increments, then using a finite multi-scale closed loop to reverse-check incompatible edges, and only reconstructs the three-dimensional displacement in the compatible subgraph after proving the optimality of the minimum modified edge set. Simultaneously, it outputs conservative states and supplementary measurement areas for areas without anchors, without closed loops, and areas where the solution failed.

[0017] This application discloses a three-dimensional reconstruction and analysis method for tunnel arch settlement survey results.

[0018] Reference Figure 1-5 A three-dimensional reconstruction and analysis method for tunnel arch settlement mapping results, specifically including: Obtain reference period records and monitoring period records from at least two point cloud sources, and convert them to a unified tunnel coordinate system based on the source identifier, period identifier, and coordinate transformation relationship; In one specific embodiment, each point cloud source has a unique source identifier within the current processing version, and each point record has a point record identifier and a period identifier. The reference period and monitoring period correspond to the period of freezing the surface geometry and the current period for performing inter-period comparisons, respectively. The coordinate transformation relationship is provided by the calibration chain or registration chain actually used in the project. The processor selects the corresponding relationship according to the source identifier, transforms the point coordinates to the same unified tunnel coordinate system, and retains the point record identifier, source identifier, period identifier, and transformation version before and after the transformation, so that any subsequent local evidence can be traced back to the original record.

[0019] When recording data at the receiving point, the processor checks whether the source identifier, period identifier, coordinate components, and coordinate transformation relationships are complete and finite. If any source lacks a traceable coordinate transformation relationship, it does not substitute it with the relationship from other sources but marks that source as having unverified coordinates. If the number of valid sources that can enter the complete main chain is less than two, the formation of multi-source fusion edge data is stopped, and the corresponding acquisition coverage area is registered as a supplementary measurement area. Point cloud sources are formed by point cloud acquisition sources with independent source identifiers and auditable calibration chains or registration chains. Subsequent processing uses source identifiers to distinguish their evidence and does not depend on specific device models.

[0020] Based on the reference period record, establish a circumferentially partitioned and circumferentially closed lining surface element diagram, and freeze the element representative position, edge specification direction and edge orthogonal basis; In one specific embodiment, the processor establishes continuous axial intervals along the axis of a unified tunnel coordinate system and establishes consecutive circumferential intervals along the circumference of the reference period lining surface. The combination of axial and circumferential intervals forms lining surface units. Both the axial and circumferential surface unit scales are positive values, determined by the reference period point spacing, the target spatial resolution, and the minimum number of local points required for each unit. If the scale is not positive or if effective units cannot be formed after division, the mapping of this processing version is blocked.

[0021] The processor establishes a stable element identifier for each lining surface element, and determines the frozen representative position of the surface element by recording valid reference period points within that element. When two elements are axially or circumferentially adjacent, a surface adjoining edge is established, and the edge tail, edge head, and edge specification direction are determined according to the stable element identifier order. The edge orthogonal basis is established during the reference period, and its three basis vectors are expressed in a unified tunnel coordinate system and frozen in the current processing version; subsequent monitoring results must not update the element representative position and the edge orthogonal basis. If a reference period point record sufficient to determine the representative position or orthogonal basis is missing, the corresponding element and its adjacent edge markers are unverified and enter the supplementary measurement area.

[0022] The two-phase point evidence is allocated according to the mutual exclusion of adjacent edges on the surface, and the relative displacement increment and uncertainty of the edge are formed based on the local inter-phase transformation of the two-end point evidence of each edge. In one specific embodiment, the processor first registers the point records used for independent displacement anchor point constraints as anchor point reserved point records, preventing them from entering the evidence allocation of any surface adjacent edges. Then, it calculates the surface distance to the support area of ​​the candidate surface adjacent edge for the remaining candidate point records, and determines the unique edge assignment sequentially using the minimum surface distance and the stable edge identifier. The surface distance is the shortest length from the surface projection position of the candidate point to the support area of ​​the candidate surface adjacent edge in the local surface coordinates of the reference period; if a finite projection position or a finite shortest length cannot be formed, the point does not enter the edge evidence. Thus, each original point record enters only the dedicated evidence area of ​​one surface adjacent edge in the same period, and will not simultaneously support another edge or displacement anchor point.

[0023] The processor perpendicularly bisects the boundary using a reference surface equidistant from the surfaces representing the end and beginning positions of an edge, dividing the exclusive evidence of an edge into end-point evidence and beginning-point evidence. Point records located on the equidistant boundary line are assigned to the side of the cell whose identifier comes first, in ascending order of end-point and beginning-point identifiers, ensuring that each assigned point record has only one edge affiliation.

[0024] For adjacent edges and the same edge from the same source and on the same surface, the processor establishes a local correspondence only between the reference period-specific point evidence and the monitoring period-specific point evidence at that edge. The local correspondence distance threshold is determined and frozen before the start of this processing version based on the local point spacing of the source, measurement uncertainty, and the inter-period search range allowed by the monitoring task. Starting with a unit transformation, the processor converts the reference period candidate points to the monitoring period according to the current transformation, searches for the nearest monitoring period point and the nearest reference period point within the threshold, retaining only the closest point pairs; when distances are equal, the point record identifier sequence is used to select the one that is closest. The processor uses the retained point pairs to estimate the local inter-period transformation using the pre-processed frozen 3D rigid body mapping model, updates the candidate correspondences, and repeats the estimation until the set of corresponding point pairs no longer changes, the transformation update amount does not exceed the convergence threshold frozen according to coordinate numerical precision, or the upper limit of the number of frozen iterations is reached.

[0025] A local intertemporal transformation is valid only if the number of corresponding point pairs reaches the minimum effective number of locally fitted point pairs frozen according to the degrees of freedom and redundancy requirements of 3D rigid body mapping, the corresponding positions are not all collinear, the local corresponding design matrix is ​​of full rank, the number of conditions does not exceed the freezing upper limit, the residuals and transformations are both finite, and the aforementioned stability conditions are met before reaching the upper limit of the number of iterations. If there are no nearest point pairs, insufficient effective point pairs, point position degradation, the design matrix is ​​not of full rank, the number of conditions exceeds the limit, the residuals are not finite, or the process is still unstable after reaching the upper limit of the number of iterations, the local intertemporal transformation at the corresponding edge source is invalid.

[0026] The processor estimates the local intertemporal transformations at the edge tail and the edge head respectively, and applies each transformation to the corresponding frozen surface unit representative position to form the three-dimensional displacements of the edge tail environment and the edge head environment under the same source:

[0027] in, Point cloud source identifier; = For the tail unit Pointing to the first unit Surface adjacent edges; and Sources respectively Local intertemporal transformations estimated on evidence from exclusive points at the tail and head of the edge; and These represent the positions of the frozen surface units at the edge tail and edge head, respectively, with the unit being length. and Sources respectively The three-dimensional displacements of the edge tail environment and the edge head environment are given in units of length.

[0028] The processor subtracts the 3D displacements of the edge's head environment and tail environment within the same frozen edge orthogonal basis to form the relative displacement increment of the source edge:

[0029] in, For source The relative displacement increment of the source edge, in units of length; For a frozen edge orthogonal basis; and Sources respectively The three-dimensional displacements of the edge head environment and the edge tail environment are given in units of length.

[0030] The 3D rigid body mapping is only used as a local operation to map the frozen representative position from the reference period to the monitoring period. The processor only subtracts the 3D displacements of the two environments in the same frozen edge orthogonal basis. The resulting relative displacement increment of the source edge is not the translation parameter of the local rigid body transformation, not the absolute intertemporal transformation of either end, nor the difference of the subsequent reconstructed displacement; the 3D rigid body mapping is not composite in the closed loop.

[0031] For each valid edge, the processor first generates a residual covariance from the local corresponding residuals, and then generates a local transformation parameter covariance from the inverse of the normal matrix of the full-rank local corresponding design matrix and the residual covariance. Subsequently, the local transformation parameter covariance is propagated to the environmental 3D displacement covariance by applying a local intertemporal transformation to the Jacobian of the frozen representative position. The joint covariance of the environmental 3D displacements of the edge tail and edge head is then propagated through the Jacobian of the subtraction within the orthogonal basis of the same frozen edge, forming the relative displacement increment covariance of the source edge. The source calibration uncertainty shared by the edge tail and edge head is only counted once in the joint covariance. If the residual degrees of freedom are insufficient, the design matrix is ​​not full rank, the normal matrix is ​​not invertible, or the Jacobian or any intermediate covariance is not finite, the source edge quantity is invalid.

[0032] The covariance of the relative displacement increment of each source edge must be a finite symmetric matrix, and a positive definite source covariance must be formed according to the same minimum eigenvalue lower bound rule as the closed-loop propagation uncertainty; if a finite positive definite source covariance cannot be formed, the source will not be included in the consistency judgment. For two valid sources, the processor records the difference between the relative displacement increments of their source edges as... = And form a quadratic form of the source difference using the difference and the sum of the positive definite covariances of the two sources:

[0033] in, For surface adjacent edges Source With source Dimensionless source difference quadratic form; and These are the relative displacement increments of the source edges from source s and source t, respectively, in units of length; It represents the difference in relative displacement increments between the two source edges, in units of length; and These are the positive definite source covariances from the two sources, expressed in units of length squared.

[0034] The total misclassification tolerance probability for source consistency is registered between 0 and 1 before processing. When the number of valid sources on the current side is at least 2, the tolerance probability is formed by equally dividing the actual number of valid source pairs compared, and the source consistency threshold is frozen by the upper tail quantile of a chi-square distribution with 3 degrees of freedom. The processor only... If the number of valid sources does not exceed this threshold, the corresponding source pair is considered consistent. If the number of valid sources is less than 2, the probability is not in the domain, or the sum of the covariances cannot form a finite positive definite matrix, a consistent source subset is not formed.

[0035] The processor enumerates all finite source subsets with at least two sources, and retains only subsets where the difference quadratic form of any pair of sources within them does not exceed the frozen source consistency threshold. For consistent source subsets, the processor first forms an information matrix summary. = and information vector = Then, candidate fusion uncertainty and candidate fusion edge relative displacement increment are formed:

[0036] in, A subset of consistent sources; For source The positive definite source edge relative displacement increment covariance, in units of length squared; For source The relative displacement increment of the source edge, in units of length; For subset The total amount of information matrix data, expressed as the negative square of the length; For subset The information vector is expressed as the negative first power of length. For subset The candidate fusion uncertainty, in units of length squared; For subset The relative displacement increment of the candidate fusion edge, in units of length.

[0037] If any source covariance, information matrix, sum of information matrices, or candidate fusion result contains non-finite quantities, or the sum of information matrices is not invertible, the corresponding source subset is invalid. When selecting a valid subset, the number of sources is compared sequentially. The matrix trace and source identifier sequence are used to determine a unique consistent source subset. If there is no valid consistent source subset containing at least two point cloud sources, the corresponding edge label is in a source insufficiency state, and the single-source result is not used to replace the multi-source fusion edge quantity. If the insufficient point evidence is only caused by insufficient point records during the monitoring period, the local correspondence and information fusion are re-executed after obtaining the newly added monitoring period point records in the new processing version; if the insufficient point evidence is caused by insufficient point records during the reference period, it remains unverified, and the newly added monitoring period point records are not used to replace the reference period point records.

[0038] In the lining surface unit diagram, a finite axial, circumferential and axial-circumferential hybrid multi-scale closed loop is generated. The relative displacement increment of the edge in each closed loop is directly converted to the corresponding closed loop root. The closed residual is accumulated according to the edge direction to form a closed residual. The closed residual is normalized according to the propagation uncertainty to determine the abnormal loop. In one specific embodiment, the processor constructs a spanning tree within each connected component based on stable cell and stable edge identifiers, forming basic closed loops from non-tree edges and unique tree paths. Then, using axial and circumferential spans that double sequentially starting from 1 and never exceeding the maximum frozen cell span before processing, it enumerates axially dominant rectangular closed loops, circumferentially dominant rectangular closed loops, axial-circumferential hybrid rectangular closed loops, and complete circumferential closed loops. Each candidate closed loop has a frozen root cell, a closed loop direction, and an ordered sequence of stable edge identifiers. Invalid edges, duplicate cells, or loops that cannot close completely are removed, and duplicate sequences are deduplicated. When the upper limit of the number of candidates is reached, a limited number of candidates are retained in ascending order of basic closed loop priority, closed loop scale, and stable closed loop identifier, and the regions corresponding to edges that did not participate in the retention of closed loops are registered as closed loop uncovered regions.

[0039] During the reference period, the closed-loop foundation is determined and frozen by the axial direction of the unified tunnel coordinate system and the reference surface direction at the root element. Each inner edge of the loop undergoes direct basis replacement only through the directional relationship between its frozen edge orthogonal basis and the closed-loop foundation relative to the unified tunnel coordinate system; basis replacement is not performed segment by segment along adjacent surface elements, nor is rotation estimated segment by segment along the surface path. When traversing the specification edges in the same direction, positive increments are taken; when traversing in the opposite direction, negative increments after direct basis replacement are taken.

[0040] The processor performs directed accumulation based on the direct basis transformation relationship and direction sign of the effective edges within the closed loop, forming a three-dimensional closed residual:

[0041] in, For closed loop The three-dimensional closed residual, in units of length; For a closed loop in a finite closed-loop ledger; The adjacent edge of the inner surface of the closed loop; For closed-loop edge traversal The direction sign is set to 1 for the same direction and negative 1 for the opposite direction. = This is a direct orthogonal coordinate transformation from an edge-orthogonal basis to a closed-loop root basis; For the edge Frozen edge orthogonal basis; As the foundation of a closed loop; This represents the relative displacement increment of the edge, in units of length.

[0042] The processor propagates the measurement uncertainties of each side to the closed-loop root basis and includes the common uncertainty of the unified coordinate relationship as a closed-loop common term only once, forming the propagated uncertainty:

[0043] in, This represents the uncertainty of closed-loop propagation, expressed in units of length squared. For the edge The relative displacement increment covariance of the edge, in units of length squared; This is the closed-loop common covariance term for the unified coordinate transformation relationship, expressed in squared length. When the unified coordinate transformation relationship is considered a frozen constant within the current processing version... Take the zero matrix; when modeling common coordinate errors separately, these errors are formed by propagation through the closed-loop global Jacobian. And it should only be added once; the same common error should not be written repeatedly into each entry. .

[0044] The processor performs deterministic positive definite transformation based on the smallest eigenvalue of the propagation uncertainty, forming a positive definite increment and a positive definite propagation uncertainty:

[0045] in, For closed loop The non-negative positive definiteness increment, in units of length squared; The lower limit of positive covariance is frozen before processing based on the coordinate numerical accuracy and the minimum discernible range of covariance, in units of length squared. for The smallest eigenvalue, expressed in units of length squared; This represents the positive definite propagation uncertainty, expressed in units of length squared. It is a 3-order identity matrix.

[0046] The processor uses positive definite propagation uncertainty to perform a quadratic measure on the closed residual, forming a normalized closed quantity:

[0047] in, For closed loop Dimensionless normalized closed-form quantity; The residual is a three-dimensional closed loop, in units of length. This represents the positive definite propagation uncertainty, expressed in units of length squared.

[0048] when Less than hour, When the two are equal or the former is greater than the latter, A value of 0 does not additionally change the propagation uncertainty. Not a finite symmetric matrix Including non-finite components, If the matrix is ​​not positive or cannot be formed into a finite invertible matrix after positive definiteness, the processor will not perform the calculation. The closed loop is marked as unverified and the corresponding area is merged into the area not covered by the closed loop.

[0049] When the number of valid retained loop closures in this batch is 0, the processor marks it as an unverified state with no loop closures, does not perform division, does not generate a single-loop false alarm tolerance probability, and does not perform abnormal loop judgment. When the number of valid retained loop closures is at least 1, the total false alarm tolerance probability registered before processing and located between 0 and 1 is divided by the number of valid retained loop closures to form the single-loop false alarm tolerance probability; the quantile of the upper tail probability in a chi-square distribution with 3 degrees of freedom equal to this single-loop false alarm tolerance probability is taken to form the theoretical loop closure threshold. When the number of stable calibration loop samples reaches the minimum number of frozen samples, the empirical loop closure threshold is formed by the empirical quantiles of samples of the same type and scale, and the larger of the theoretical threshold and the empirical threshold is taken; when the samples are insufficient, only the theoretical threshold is used and it is marked as uncalibrated. The processor only... Valid loops that are strictly greater than the freeze loop threshold are identified as abnormal loops, while loops that are equal to the threshold are not marked as abnormal loops.

[0050] Based on the participation relationship between abnormal cycles and modifiable edges and the modification cost, the set of modified edges that hit each abnormal cycle and have the minimum total cost is obtained. Only after proving that the set of modified edges is optimal are the corresponding edges isolated and the closed cycle is re-examined to form a compatible subgraph. In one specific embodiment, the processor extracts surface adjacent edges from the anomalous loop that have valid relative displacement increments, participate in the anomalous loop, and are not locked by independent displacement anchor constraints, forming a finite set of modifiable edges. The positive modification cost of each modifiable edge is formed by weighting the ascending order of the number of valid point cloud sources, the information matrix trace, and the number of participants in the non-anomaly preserved loop according to the frozen positive weight; when any original evidence value is equal, the consecutive positions are determined by ascending order of the stable edge identifier to ensure that the cost and subsequent comparisons remain definite.

[0051] The processor retains a candidate subset of all anomalous cycles within the power set of the finite set of modifiable edges, forming a family of feasible sets of modifiable edges:

[0052] in, To make it feasible to modify the family of edge sets; It is a finite set of anomalous cycles; It is a finite set of modifiable edges that participate in at least one anomalous cycle and are not locked. For abnormal loop The set of modifiable edges contained therein; for The candidate subset. When empty, the processor is marked as having no feasible modifications.

[0053] The processor selects a subset of candidates. The comparison vector consists of the total cost, the number of edges, and the stable edge identifier sequence. = In the family of non-empty feasible modified edges, compare the vectors lexicographically to determine the unique minimum set of modified edges:

[0054] in, For the edge The limited cost of positive modification; The number of edges contained in the candidate subset; The sequence is sorted in ascending order by stable edge identifiers; For candidate subsets The three comparison vectors; superscript Indicates by The three items are compared lexicographically from left to right; Let be the set of modified edges that have been proven to be globally optimal under all constraints.

[0055] The processor establishes a participation relationship table between abnormal cycles and modifiable edges. For any abnormal cycle, the corresponding... When the set is empty, it is directly marked as a state with no feasible modifications. In other cases, branching and bounding begin with the empty set as the root: first, select anomalous cycles that have not yet been hit by sorting them in ascending order of the number of modifiable edges and stable loop identifiers; then, establish branches to include candidate edges in ascending order of positive modification cost, descending order of the number of participating anomalous cycles, and ascending order of stable edge identifiers. For anomalous cycles that have not yet been hit, select cycles that do not share modifiable edges by stable loop identifiers, and add the lowest positive modification cost of each cycle to the cost of the currently selected edge to form a lower bound; prune the branch if the lower bound and the achievable subsequent parallel results are not better than the current optimal feasible solution.

[0056] The current optimal feasible solution is marked only after all search branches have been processed or pruned by a provable lower bound. When the number of search nodes reaches the freeze limit or the runtime reaches the freeze limit, if there are still unprocessed branches, they are marked as unresolved optimization states. Temporary candidate solutions are not considered as the minimum set of modifiable edges, and no modifiable edges are isolated. When there are no abnormal cycles, If the set is empty, proceed directly to the closed-loop re-examination; if an abnormal cycle exists and there is no feasible solution, stop deleting edges.

[0057] Reconstruct each connected component based on the relative displacement increment of the remaining edges of the compatible subgraph. When the reconstructed relation is full rank, the condition number is qualified, and the solution is finite, the connected component with valid and consistent independent displacement anchor constraints is marked as an absolutely valid state, the connected component that originally did not have independent displacement anchor constraints and was subject to zero mean constraints is marked as a relative state only, and the remaining connected components are marked as unverified states. In one specific embodiment, the processor only... It has been proven that, in the optimal scenario, surface adjacent edges are isolated according to stable edge identifiers, while retaining the point record identifier, source identifier, and isolation reason of the isolated edge. After each round of isolation, a complete finite multi-scale closed-loop set is regenerated from all remaining valid edges using the same stable unit identifier, stable edge identifier, span sequence, candidate sorting, and upper limit of the candidate number as in the initial generation; it is not permissible to only recalculate the basic cycles of the original spanning tree or only check the old cycles directly affected by the deleted edges.

[0058] If abnormal cycles are still found during re-examination, they are added to the abnormal cycle ledger, and the minimum modified edge search is re-executed. Only after proving optimality again is at least one previously unisolated edge isolated. The loop terminates successfully when none of the remaining registered closed cycles exceed the frozen closed cycle threshold and at least one connected component contains a valid retained closed cycle; it terminates if the number of isolated edges reaches the original total number of valid edges, no new modified edges are added in a consecutive round, or no connected component contains a valid retained closed cycle. Only the remaining edges that participate in at least one valid retained closed cycle are included in the compatible subgraph; the regions corresponding to the remaining edges that do not participate in a valid retained closed cycle are merged into the closed-cycle uncovered region and are not used for displacement reconstruction.

[0059] For each remaining edge in the compatible subgraph, the processor uses the same positive commutation basis to transform the relative displacement increment and its uncertainty to a unified tunnel coordinate system. Only for remaining edges whose transformed uncertainty is a finite positive definite matrix, the processor inverts the matrix to form information weights. Subsequently, for each connected component, the difference between the 3D displacement to be reconstructed at the edge's head and tail is used to approximate the relative displacement increment in the unified coordinate system. Anchor point displacement differences are calculated assuming the candidate anchor point set is not empty and all are valid and consistent, thus forming edge residuals. and anchor point residual :

[0060] in, For compatible subgraph edges = The three-dimensional edge residuals, in units of length; and These are the three-dimensional displacements to be reconstructed for the tail element and the head element, respectively, in units of length. This is an orthogonal transformation that directly converts an edge-orthogonal basis to a unified tunnel coordinate system; This represents the relative displacement increment of the edge, in units of length. anchor point The three-dimensional anchor point residuals, in units of length; anchor point The three-dimensional absolute displacement, in units of length; Surface units associated with anchor points.

[0061] The processor will process the information matrix The weighted quadratic term under is denoted as = We obtain the reconstructed 3D displacement set of connected components by weighting the edge residuals and anchor residuals using the edge information matrix and anchor information matrix, respectively.

[0062] in, A stable index for currently compatible connected components; The set of remaining edges in the current compatible connected component that participate in at least one valid preserved loop; The information matrix is ​​formed by the edge measurement covariance, with units of length negative square. For index The set of independent displacement anchor points formed after all candidate anchor points in the corresponding connected components are not empty and are valid and consistent. When the candidate anchor point set is empty, it is explicitly selected. = ; This is the anchor point information matrix, with units of length negative squared. This is the reconstructed three-dimensional displacement set of the connected component.

[0063] When the candidate anchor point set is not initially empty, the processor only forms the anchor point set after all candidate anchor points are fully three-dimensional, have finite uncertainty, and are mutually consistent. Write it into the objective function, and output the absolutely valid state when the reconstructed relation is full rank, the number of conditions does not exceed the upper limit of the freeze before processing, and the solution result is finite; if the candidate anchor point exists but is invalid or conflicting, directly output the unverified state, without considering the other conditions. Set to an empty set and do not enter the zero-mean branch. The processor only allows the candidate anchor set to be empty if it was originally empty. = This makes the anchor weighting term in the objective function equal to 0, without fabricating fixed nodes, and instead focuses on all nodes in the connected component. The three components are subject to normative constraints with a mean of zero. When the reconstructed relation is full rank, the condition number is qualified, and the solution result is finite after adding the constraint, the output is only the relative state, and the generation of absolute displacement alarm is prohibited.

[0064] Anchored and unanchored branches are used together to check for valid loop closures, the rank of reconstructed relations, the condition number, and the finiteness of solutions. Multiple inconsistent anchor points indicate an anchor point conflict state; anchor points not reaching three dimensions or with non-finite uncertainty indicate an invalid anchor point state; reconstructed relations not reaching rank indicate a rank deficiency state; condition number exceeding the limit indicates a numerically unstable state; non-finite solution results indicate a solution failure state; components containing only elements without connected remaining edges indicate an isolated component state; components not containing valid retained loops indicate a non-looping component state. All of the aforementioned states are merged into the unverified state, without outputting a definite three-dimensional displacement, and unverified is not interpreted as zero deformation.

[0065] Outputs 3D displacement, modified edge set, closed-loop uncovered area, connected component status, and supplementary measurement area.

[0066] In one specific embodiment, the processor creates a processing version for each execution and associates it with a unified tunnel coordinate system, a frozen surface unit graph, point record allocation relationships, a stable closed-loop identifier, a frozen closed-loop threshold, a modified edge set, and the connected component state. The absolutely valid state outputs the three-dimensional displacement within the unified tunnel coordinate system; the relative state only outputs the three-dimensional relative displacement under the zero-mean specification; the unverified state only outputs the cause and the affected area, without outputting a definite three-dimensional displacement.

[0067] The processor merges the uncovered loop closure area, the adjacent area of ​​the isolated modified edge, and the area corresponding to the unverified connected components into a supplementary testing area. After obtaining the newly added point records in the supplementary testing area, its source identifier, period identifier, and coordinate transformation relationship are retained. The subsequent steps are re-executed from the point record allocation starting with the new processing version, and the previous processing version, status, and status change records are retained. When supplementary testing data is not obtained, the supplementary testing area and its unverified reasons are still output, and the missing loop closure evidence is not replaced by interpolation of adjacent valid areas.

[0068] Furthermore, the conversion includes: recording the registration point identifier, source identifier, period identifier, and coordinate transformation version for each point; According to the source identifier, call the corresponding coordinate transformation relationship to convert the reference period record and the monitoring period record to a unified tunnel coordinate system; If any of the following conditions exist: missing point records, missing coordinate transformation relationships, or non-finite quantities, the corresponding point cloud source will be marked as having unverified coordinates, and the generation of relative displacement increments will stop when there are fewer than two valid point cloud sources.

[0069] Specifically, the point record identifier is used to associate the original record, the unified coordinate point record, and subsequent edge evidence; the source identifier is used to select the corresponding coordinate transformation relationship; the period identifier is used to distinguish between the reference period and the monitoring period; and the coordinate transformation version is used to register the calibration chain or registration chain used in this conversion. These identifiers are retained before and after the conversion, ensuring that any edge quantity can be traced back to the input point record.

[0070] The processor checks each point record, coordinate transformation relationship, and coordinate component. When a missing item or non-finite quantity is found, it does not use coordinate transformation relationships from other sources to replace it, but marks the corresponding source as unverified. When there are fewer than two valid point cloud sources, it stops multi-source edge quantity formation and registers the affected area.

[0071] Furthermore, the lining surface unit diagram includes: surface units divided along the axial direction of the unified tunnel coordinate system and the circumferential direction of the lining surface during the reference period, and surface adjacent edges that connect axially adjacent surface units and circumferentially adjacent surface units respectively. Establish stability identifiers for surface elements and adjacent edges, and determine the edge specification direction according to the stability element identifiers at both ends of the edge; The representative position of the element is determined by the reference period point record, and an edge orthogonal basis is established based on the axis of the unified tunnel coordinate system and the surface direction of the reference period. Surface elements and their adjacent edges that cannot be determined by either the representative position of the element or the edge orthogonal basis are marked as unverified.

[0072] Specifically, the processor establishes a continuous axial interval along the axis of the unified tunnel coordinate system and establishes a circumferential interval with the beginning and end connected along the circumferential direction of the reference period lining surface. The two are combined to form a surface unit. The axial adjacent units and the circumferential adjacent units are connected respectively to obtain a circumferentially closed surface adjacency relationship.

[0073] The processor establishes stable identifiers for cells and adjacent edges on the surface, and determines the edge tail, edge head, and edge specification direction based on the stable cell identifiers at both ends of the edge. The cell representative position is determined by the reference period valid point record, and the edge orthogonal basis is determined by the axis of the unified tunnel coordinate system and the surface direction of the reference period; if any one of these cannot be determined, the corresponding cell and adjacent edges remain unverified.

[0074] Furthermore, when forming the relative displacement increment and uncertainty of the edge: the anchor point retention record used for independent displacement anchor point constraint is excluded, and the remaining point records are uniquely assigned according to the minimum surface distance from the adjacent edge support area of ​​the candidate surface. When the distances are the same, the stable edge identifier is used for adjudication. Using equidistant boundary lines representing positions at both ends of the edge, the allocated point records are divided into edge tail point evidence and edge head point evidence; According to the point cloud source establishing a local correspondence between the corresponding edge endpoint evidence in two periods, the local inter-period transformation of the edge tail and the local inter-period transformation of the edge head are estimated respectively and applied to the representative position of the corresponding unit. The difference is made in the same edge orthogonal basis to form the relative displacement increment of the source edge and the source uncertainty of each point cloud source.

[0075] Specifically, the processor first excludes anchor point retention point records, and then determines the unique edge assignment based on the minimum surface distance from the candidate point to the adjacent edge support area; when distances are tied, the stable edge identifier is used for adjudication. The point record identifier, stable edge identifier, and assignment results constitute a point-to-edge audit table, which is used to check whether point evidence in the same period has been reused between edges.

[0076] The processor distinguishes between edge tail and edge head evidence within the support region of each edge according to equidistant boundary lines, and establishes a local correspondence only between two periods-specific evidence from the same source and the same edge. Two local inter-period transformations are applied to the corresponding unit representative positions, and the results are subtracted in the same edge orthogonal basis to obtain the edge quantity and uncertainty of that source.

[0077] Furthermore, the relative displacement increment of the source edge of each point cloud source is judged in terms of consistency according to the source uncertainty, forming a consistent source subset containing at least two point cloud sources; Each consistent source subset is sorted in descending order of the number of sources, ascending order of the trace of the fusion uncertainty matrix, and ascending order of the source identifier sequence. The consistent source subsets that are ranked first are selected and fused into edge relative displacement increment and uncertainty according to information weight. If any edge cannot form a local correspondence, the local transformation design matrix is ​​not of full rank, or any of the aforementioned consistent source subsets does not exist, the adjacent edge of the corresponding surface will be marked as unverified. If insufficient point evidence is caused solely by insufficient point records during the monitoring period, local correspondence and information fusion are re-executed after acquiring new monitoring period point records. If insufficient point evidence is caused solely by insufficient reference period point records, it remains unverified and is not replaced by new monitoring period point records.

[0078] Specifically, the processor checks the pairwise consistency of source edge quantities using source uncertainty, enumerates consistent source subsets that contain at least two valid sources and whose internal comparisons all pass, and determines unique subsets in turn by the number of sources, the trace of the fusion uncertainty matrix, and the source identifier sequence, and then forms fusion edge quantities and uncertainties by information weights.

[0079] If any edge cannot form a local correspondence, the local transformation design matrix is ​​not of full rank, or there is no consistent source subset, the corresponding edge remains unverified. If insufficient point evidence is solely due to insufficient monitoring period records, the monitoring period records can be added in the new processing version and the calculation recalculated; if the reference period records are insufficient, the added monitoring period records will not replace the reference period evidence.

[0080] Furthermore, when determining the abnormal loop: a basic closed loop is generated in each connected component, and axial, circumferential, axial-circumferential mixed and complete circumferential closed loops are generated according to the finite axial span and circumferential span. Candidate closed loops with any of the defects of invalid edges, duplicate units, and inability to close are eliminated, and the root unit, direction and stable closed loop identifier of the retained closed loop are frozen. When the number of candidate closed loops exceeds the upper limit of the number of frozen candidates, closed loops are retained in order of priority of basic closed loops, in ascending order of closed loop scale, and in ascending order of stable closed loop identifier. The areas not covered by the retained closed loops are defined as closed loop uncovered areas. The relative displacement increments and uncertainties of the edges within the closed loop are directly converted to the basis of the closed loop and propagated and accumulated according to the edge direction. Only for closed loops where the closure residuals and propagation uncertainties are finite and the propagation uncertainties can be positive definite, a normalized closure quantity is formed. Loops whose normalized closure values ​​exceed the frozen loop threshold are identified as abnormal loops. The frozen loop threshold is the larger of the theoretical threshold for freezing before processing and the empirical threshold formed when the sample conditions are met.

[0081] Specifically, the closed-loop candidates consist of basic closed loops, finite axial span closed loops, finite circumferential span closed loops, axial hybrid closed loops, and complete circumferential closed loops in the current valid surface diagram. The span, upper limit of the number of candidates, root element, direction, and stable closed-loop identifier are all frozen before this judgment, and defective candidates are eliminated.

[0082] Each inner edge of a loop is directly converted from the edge orthogonal basis to the closed-loop root basis and propagated and accumulated along the ergodic direction. The closure residual is normalized only when the propagation uncertainty is finite and can be positive definite. When the number of candidates exceeds the upper limit, they are retained according to the freezing priority. Regions not covered by the retained closed loops are registered separately and are not interpreted as non-variable.

[0083] Furthermore, when forming the modified edge set and compatible subgraph: the surface adjacent edges that participate in the abnormal loop, have valid relative displacement increments and are not locked by independent displacement anchor point constraints are registered as modifiable edges. The modification cost is formed by weighting the number of valid point cloud sources, information matrix traces and the number of non-abnormal closed loops in ascending order. When the original values ​​of each item are equal, the consecutive positions are determined by the ascending order of the stable edge identifier. Search for a candidate set that hits all anomalous cycles in a finite subset of modifiable edges. Compare the candidate sets in order of total cost, number of edges, and stable edge identifier sequence. Determine the set of modified edges by exhausting the candidate set through branch and bound and pruning search branches that have no possibility of improvement. When the search resource limit is reached before the search is completed, output the unresolved optimization state and do not isolate the modifiable edges; When the modified edge set has been proven to be optimal, the corresponding edge is isolated and the closed loop of all remaining valid edges is regenerated. The process of identifying abnormal loops and obtaining the modified edge set is repeated until all remaining closed loops are non-abnormal. The remaining edges that participate in the valid closed loops are then combined into a compatible subgraph.

[0084] Specifically, the evidence values ​​for the modification cost are first converted in ascending order; when any original value is equal, the stable edge identifiers are used to determine the consecutive positions of equal values ​​in ascending order, so that the modification cost and candidate comparisons have unique results under the same input. The search compares the total cost, the number of edges, and the sequence of stable edge identifiers in turn.

[0085] The current feasible solution serves only as an upper bound for the search. Optimality is only proven after all branches have been exhausted or the solution has been pruned by a valid lower bound. If the resource limit is reached first, all edges are preserved and the optimization remains unsolved. Only after optimality is proven are the corresponding edges isolated, and the closed loop is regenerated with all remaining valid edges until a compatible subgraph is formed or a failure state is entered.

[0086] Furthermore, when reconstructing the connected components and determining the connected component state: the relative displacement increment and uncertainty of each remaining edge are converted to a unified tunnel coordinate system according to the same positive commutation basis, and only the inverse matrix of the remaining edge whose uncertainty after conversion is a finite positive definite matrix is ​​taken to form information weights. Based on the displacement difference residuals and information weights corresponding to the remaining edges, a weighted least squares reconstruction relationship is established for each connected component. When the candidate anchor point set is not empty and all anchor points are full three-dimensional, with finite uncertainty and mutual consistency, an independent displacement anchor point constraint is added; when the candidate anchor point set is empty, a zero-mean constraint is applied to the three-dimensional displacement of the connected components. The two branches mentioned above are jointly checked for the validity of closed loops, the reconstruction of relation rank, the condition number and the finiteness of solutions. When the check passes, they are marked as absolutely valid state and only relative state, respectively. When any of the following conditions exist, such as check failure, invalid anchor point, or anchor point conflict, it is marked as unverified state.

[0087] Specifically, the edge quantity and uncertainty of each remaining edge are transformed to a unified tunnel coordinate system using the same positive commutative basis; the inverse is taken only when the transformed uncertainty is a finite positive definite matrix to form information weights. Based on this, the processor establishes a weighted least squares reconstruction relationship of the difference between the edge head displacement and the edge tail displacement.

[0088] Independent anchor point constraints are added when the candidate anchor point set is not empty and all anchor points are full-dimensional, finite, and mutually consistent; when the candidate anchor point set is empty, a three-dimensional displacement zero-mean constraint is applied. Both branches jointly check the validity of loop closure, reconstruct the relation rank, condition number, and the finiteness of the solution. Invalid anchor points, conflicts, and failure of joint checks all enter an unverified state.

[0089] Furthermore, a processing version is established for each processing step, and the unified tunnel coordinate system, lining surface unit diagram, point record allocation relationship, frozen loop closure threshold, modified edge set and connected component status are associated with the processing version. For absolutely valid states, output the three-dimensional displacement in the unified tunnel coordinate system; for only relative states, output the three-dimensional relative displacement under zero mean constraint and prohibit the formation of absolute displacement alarms; for unverified states, output the state cause and do not output definite displacement. The areas not covered by the closed loop, the adjacent areas of the isolated edge, and the areas corresponding to the unverified state are merged into the supplementary test area. After obtaining the new point records, a new processing version is established and the processing starts from the mutual exclusion allocation of point records. At the same time, the previous processing version and state change records are retained.

[0090] Specifically, the processing version binds the unified coordinate system, frozen surface map, point record allocation relationship, loop closure threshold, modified edge set, and connected component state as immutable associated records. Absolutely valid states output 3D displacement in the unified coordinate system; relative states only output zero-mean relative displacement; unverified states only output the cause and region.

[0091] The processor merges the uncovered closed-loop areas, adjacent areas of isolated edges, and areas corresponding to unverified states into a supplementary test area. After acquiring new point records, a new processing version is created, and processing restarts from the point record mutual exclusion allocation; the new version does not overwrite the previous version, and state changes and output limitations are all retained in the version log.

[0092] The above content is merely an example and illustration of the concept of the present invention. Those skilled in the art can make various modifications or additions to the specific embodiments described or use similar methods to replace them, as long as they do not deviate from the concept of the invention, they should all fall within the protection scope of the present invention.

[0093] In the description of this specification, expressions such as "an embodiment," "example," and "specific example" refer to a specific feature, structure, material, or characteristic described in connection with that embodiment or example, which is included in at least one embodiment or example of the present invention. In this specification, illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples.

[0094] The preferred embodiments of the present invention disclosed above are merely illustrative of the invention. These preferred embodiments do not exhaustively describe all details, nor do they limit the invention to any specific implementation. Clearly, many modifications and variations can be made based on the content of this specification. This specification selects and specifically describes these embodiments to better explain the principles and practical applications of the invention, thereby enabling those skilled in the art to better understand and utilize the invention.

Claims

1. A three-dimensional reconstruction and analysis method for tunnel arch settlement survey results, characterized in that, The method includes: acquiring reference period point records and monitoring period point records from at least two point cloud sources, and converting them to a unified tunnel coordinate system based on the source identifier, period identifier, and coordinate transformation relationship; Based on the reference period record, establish a circumferentially partitioned and circumferentially closed lining surface element diagram, and freeze the element representative position, edge specification direction and edge orthogonal basis; The two-phase point evidence is allocated according to the mutual exclusion of adjacent edges on the surface, and the relative displacement increment and uncertainty of the edge are formed based on the local inter-phase transformation of the two-end point evidence of each edge. In the lining surface unit diagram, a finite axial, circumferential and axial-circumferential hybrid multi-scale closed loop is generated. The relative displacement increment of the edge in each closed loop is directly converted to the corresponding closed loop root. The closed residual is accumulated according to the edge direction to form a closed residual. The closed residual is normalized according to the propagation uncertainty to determine the abnormal loop. Based on the participation relationship between abnormal cycles and modifiable edges and the modification cost, the set of modified edges that hit each abnormal cycle and have the minimum total cost is obtained. Only after proving that the set of modified edges is optimal are the corresponding edges isolated and the closed cycle is re-examined to form a compatible subgraph. Reconstruct each connected component based on the relative displacement increment of the remaining edges of the compatible subgraph. When the reconstructed relation is full rank, the condition number is qualified, and the solution is finite, the connected component with valid and consistent independent displacement anchor constraints is marked as an absolutely valid state, the connected component that originally did not have independent displacement anchor constraints and was subject to zero mean constraints is marked as a relative state only, and the remaining connected components are marked as unverified states. Outputs 3D displacement, modified edge set, closed-loop uncovered area, connected component status, and supplementary measurement area.

2. The method for three-dimensional reconstruction and analysis of tunnel arch settlement mapping results according to claim 1, characterized in that, The conversion includes: recording the registration point identifier, source identifier, period identifier, and coordinate transformation version for each point; According to the source identifier, call the corresponding coordinate transformation relationship to convert the reference period record and the monitoring period record to a unified tunnel coordinate system; If any of the following conditions exist: missing point records, missing coordinate transformation relationships, or non-finite quantities, the corresponding point cloud source will be marked as having unverified coordinates, and the generation of relative displacement increments will stop when there are fewer than two valid point cloud sources.

3. The method for three-dimensional reconstruction and analysis of tunnel arch settlement mapping results according to claim 1, characterized in that, The lining surface unit diagram includes: surface units divided along the axial direction of the unified tunnel coordinate system and the circumferential direction of the lining surface during the reference period, and surface adjacent edges that connect axially adjacent surface units and circumferentially adjacent surface units respectively; Establish stability identifiers for surface elements and adjacent edges, and determine the edge specification direction according to the stability element identifiers at both ends of the edge; The representative position of the element is determined by the reference period point record, and an edge orthogonal basis is established based on the axis of the unified tunnel coordinate system and the surface direction of the reference period. Surface elements and their adjacent edges that cannot be determined by either the representative position of the element or the edge orthogonal basis are marked as unverified.

4. The method for three-dimensional reconstruction and analysis of tunnel arch settlement mapping results according to claim 1, characterized in that, When forming the relative displacement increment and uncertainty of the edge: exclude the anchor point retention record used for independent displacement anchor point constraint, and uniquely assign the remaining point records according to the minimum surface distance from the adjacent edge support area of ​​the candidate surface. When the distances are the same, the stable edge identifier shall be used for adjudication. Using equidistant boundary lines representing positions at both ends of the edge, the allocated point records are divided into edge tail point evidence and edge head point evidence; According to the point cloud source establishing a local correspondence between the corresponding edge endpoint evidence in two periods, the local inter-period transformation of the edge tail and the local inter-period transformation of the edge head are estimated respectively and applied to the representative position of the corresponding unit. The difference is made in the same edge orthogonal basis to form the relative displacement increment of the source edge and the source uncertainty of each point cloud source.

5. The method for three-dimensional reconstruction and analysis of tunnel arch settlement mapping results according to claim 4, characterized in that, The relative displacement increment of the source edge of each point cloud source is judged for consistency according to the source uncertainty, forming a consistent source subset containing at least two point cloud sources; The consistent source subsets are sorted in descending order of the number of sources, in ascending order of the trace of the fusion uncertainty matrix, and in ascending order of the source identifier sequence. The consistent source subsets that are ranked first are selected and fused into edge relative displacement increment and uncertainty according to information weight. If any edge cannot form a local correspondence, the local transformation design matrix is ​​not of full rank, or any of the aforementioned consistent source subsets does not exist, the adjacent edge of the corresponding surface will be marked as unverified. If insufficient point evidence is caused solely by insufficient point records during the monitoring period, local correspondence and information fusion are re-executed after acquiring new monitoring period point records. If insufficient point evidence is caused solely by insufficient reference period point records, it remains unverified and is not replaced by new monitoring period point records.

6. The method for three-dimensional reconstruction and analysis of tunnel arch settlement mapping results according to claim 1, characterized in that, When identifying the abnormal loop: generate basic closed loops, finite axial and circumferential closed loops, axial-circumferential mixed closed loops and complete circumferential closed loops according to the connected components; remove candidate closed loops containing invalid edges, duplicate elements, or defects that cannot be closed; freeze the root element, direction and stable closed loop identifier of the retained closed loops. When the number of candidate closed loops exceeds the upper limit of the number of frozen candidates, they are retained in order of priority of basic closed loops, in ascending order of closed loop scale, and in ascending order of stable closed loop identifier. Areas not covered by the retained closed loops are recorded as closed loop uncovered areas. The relative displacement increments and uncertainties of the edges within the closed loop are directly converted to the basis of the closed loop and propagated and accumulated according to the edge direction. Only for closed loops where the closure residuals and propagation uncertainties are finite and the propagation uncertainties can be positive definite, a normalized closure quantity is formed. Loops whose normalized closure values ​​exceed the frozen loop threshold are identified as abnormal loops. The frozen loop threshold is the larger of the theoretical threshold for freezing before processing and the empirical threshold formed when the sample conditions are met.

7. The method for three-dimensional reconstruction and analysis of tunnel arch settlement mapping results according to claim 1, characterized in that, When forming the modified edge set and compatible subgraph: the surface adjacent edges that participate in the abnormal loop, have valid relative displacement increments and are not locked by independent displacement anchor point constraints are registered as modifiable edges. The modification cost is formed by weighting the ascending order of the number of valid point cloud sources, information matrix traces and the number of non-abnormal closed loops. When the original values ​​are equal, the consecutive positions are determined by the ascending order of the stable edge identifier. Search for a candidate set that hits all anomalous cycles in a finite subset of modifiable edges. Compare the candidate sets in order of total cost, number of edges, and stable edge identifier sequence. Determine the set of modified edges by exhausting the candidate set through branch and bound and pruning search branches that have no possibility of improvement. When the search resource limit is reached before the search is completed, output the unresolved optimization state and do not isolate the modifiable edges; When the modified edge set has been proven to be optimal, the corresponding edge is isolated and the closed loop of all remaining valid edges is regenerated. The process of identifying abnormal loops and obtaining the modified edge set is repeated until all remaining closed loops are non-abnormal. The remaining edges that participate in the valid closed loops are then combined into a compatible subgraph.

8. The method for three-dimensional reconstruction and analysis of tunnel arch settlement mapping results according to claim 1, characterized in that, When reconstructing the connected components and determining the connected component state: the relative displacement increment and uncertainty of each remaining edge are converted to a unified tunnel coordinate system according to the same positive commutation basis, and only the inverse matrix of the remaining edge whose uncertainty after conversion is a finite positive definite matrix is ​​taken to form information weights. Based on the displacement difference residuals and information weights corresponding to the remaining edges, a weighted least squares reconstruction relationship is established for each connected component. When the candidate anchor point set is not empty and all anchor points are full three-dimensional, with finite uncertainty and mutual consistency, an independent displacement anchor point constraint is added; when the candidate anchor point set is empty, a zero-mean constraint is applied to the three-dimensional displacement of the connected components. The branches with independent displacement anchor point constraints and the branches with zero mean constraints are jointly checked for valid loop closure, reconstructed relation rank, condition number and finiteness of solution. When the check passes, they are marked as absolutely valid state and only relative state, respectively. When any of the following conditions exist, such as check failure, invalid anchor point, or anchor point conflict, it is marked as unverified state.

9. The method for three-dimensional reconstruction and analysis of tunnel arch settlement mapping results according to claim 1, characterized in that, To create a processing version for each processing step, the unified tunnel coordinate system, lining surface unit diagram, point record allocation relationship, frozen loop closure threshold, modified edge set and connected component status are associated with the processing version. For absolutely valid states, output the three-dimensional displacement in the unified tunnel coordinate system; for only relative states, output the three-dimensional relative displacement under zero mean constraint and prohibit the formation of absolute displacement alarms; for unverified states, output the state cause and do not output definite displacement. The areas not covered by the closed loop, the adjacent areas of the isolated edge, and the areas corresponding to the unverified state are merged into the supplementary test area. After obtaining the new point records, a new processing version is established and the processing starts from the mutual exclusion allocation of point records. At the same time, the previous processing version and state change records are retained.

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