Tunnel lining whole cycle deformation monitoring and analysis method based on time sequence point cloud

Abstract

The present application relates to the technical field of tunnel lining whole cycle monitoring, in particular to a kind of tunnel lining whole cycle deformation monitoring and analysis method based on time sequence point cloud.First, each period point cloud is registered and projected to unified space index grid, the Green-Lagrange strain tensor of each grid point is calculated by displacement field, and time sequence deformation tensor field is constructed;Then, the tensor sequence of each spatial position is regarded as the curve on Riemann manifold, it is mapped to tangent space by logarithmic mapping, the future tangent space vector is predicted using multivariate autoregressive model, and then it is restored to predicted deformation tensor by exponential mapping;Finally, the engineering strain index of predicted tensor is calculated, after comparing with threshold value, the spatial clustering of over-limit area is carried out, and early warning information is output.The present application respects the nonlinear geometric structure of strain tensor, realizes the full section, high-precision space-time prediction of tunnel lining deformation, and provides reliable basis for structure safety evaluation.

Description

Technical Field

[0001] This invention relates to the field of tunnel lining full-cycle monitoring technology, and more specifically, to a method for monitoring and analyzing tunnel lining full-cycle deformation based on time-series point clouds. Background Technology

[0002] During operation, tunnel lining structures are susceptible to gradual deformation due to various factors, including surrounding foundation excavation, surface loading, train vibration, and uneven ground settlement. If this deformation exceeds permissible limits, it can lead to safety accidents such as lining cracking, water leakage, and even structural instability. Therefore, high-precision monitoring and trend prediction of tunnel lining deformation are crucial technical means to ensure safe tunnel operation. Currently, tunnel lining deformation monitoring primarily employs the following technical approaches:

[0003] Traditional surveying methods, such as total stations and levels, involve setting up discrete monitoring points within the tunnel and periodically measuring the deformation data at these points. However, this method results in sparse monitoring points, making it difficult to comprehensively reflect the continuous deformation field of the lining surface. Furthermore, it is significantly affected by human factors, leading to low monitoring efficiency.

[0004] More importantly, tunnel lining deformation is a typical spatiotemporal coupled process. Most existing methods are limited to static analysis of deformation at a single moment or simple linear fitting of time series data from a single monitoring point (such as least squares regression or exponential smoothing), lacking the ability to model the time series of high-dimensional nonlinear data like the deformation tensor. The deformation tensor, as a complete mathematical object describing the strain state at a point (including circumferential normal strain, longitudinal normal strain, and shear strain), has a value space that is a symmetric positive definite matrix manifold, belonging to a nonlinear space. Traditional time series analysis methods (such as vector autoregression) are only applicable to Euclidean space; directly applying them to tensor data would destroy its inherent geometric structure, leading to a decrease in prediction accuracy.

[0005] Therefore, how to construct a tunnel lining deformation analysis method that can handle the nonlinear geometric structure of tensor data and realize spatiotemporal integrated prediction is a technical problem that urgently needs to be solved in this field. Summary of the Invention

[0006] The purpose of this invention is to provide a method for monitoring and analyzing the full-cycle deformation of tunnel lining based on time-series point clouds, so as to solve the above-mentioned technical problems.

[0007] To achieve the above objectives, the embodiments of this application provide the following technical solutions:

[0008] This application provides a method for monitoring and analyzing the full-cycle deformation of tunnel lining based on time-series point clouds. The method includes: Step S1, acquiring three-dimensional point cloud data of the tunnel lining surface at multiple time-series moments, registering the three-dimensional point cloud data, and generating a gridded lining surface point set with a unified spatial index (u,v) by projecting the registered point cloud data onto a cylindrical surface, where u is the circumferential angle parameter and v is the longitudinal mileage parameter, and the gridded lining surface point set defines the spatial sampling position shared by all time-series moments; Step S2, for each time... At time step S2, the original point cloud data is interpolated to each grid point of the gridded lining surface point set to obtain the three-dimensional spatial coordinates of each grid point at that time step. Then, the displacement field is calculated based on the three-dimensional spatial coordinates of each grid point at that time step and the initial time step, and the Green-Lagrange strain tensor A is calculated for each grid point based on the displacement field to construct the deformation tensor field at that time step. Step S3: Align the deformation tensor fields of multiple time steps obtained in step S2 according to spatial indices. For each spatial index (u,v), the corresponding time-series deformation tensor sequence is obtained. Viewed as a Riemannian manifold The curve on the curve is used to map each tensor to the tangent space at the initial time step through logarithmic mapping to obtain a tangent space vector sequence. The evolution of this tangent space vector sequence is then fitted based on a multivariate autoregressive model, and finally, the predicted deformable tensor is obtained through exponential mapping. Step S4: Based on the predicted deformation tensor Calculate the engineering deformation index, compare the engineering deformation index with a preset threshold, perform spatial clustering on spatial indices that exceed the preset threshold, and output the deformation warning area and predicted deformation value.

[0009] Optionally, the Green-Lagrange strain tensor is defined as ,in For deformation gradient, For unit tensors, It is a 2×2 symmetric positive definite matrix, whose tensor elements include circumferential normal strain, longitudinal normal strain and shear strain.

[0010] Optionally, the logarithmic mapping and exponential mapping described in step S3 are both implemented based on the geodesic distance between tensors, specifically as follows:

[0011] Define geodesic distance for measuring Riemannian manifolds The difference between the two deformation tensors, the Riemannian manifold Let the space be the space formed by all 2×2 symmetric positive definite matrices;

[0012] For any two deformable tensors and Its geodetic distance is:

[0013] ;

[0014] in, and For two arbitrary deformation tensors, For matrix logarithm operations, For the trace operation of a matrix, For deformation tensor The square root inverse matrix;

[0015] With the initial deformation tensor As a reference point, the initial deformation tensor This refers to the deformable tensor corresponding to the spatial index in the deformable tensor field constructed at the first time step in step S2;

[0016] Logarithmic mapping transforms the tensor at any given time step. Mapping to the tangent space of the reference point yields the tangent space vector. ,in For step S2 at the timing time The deformable tensor corresponding to the spatial index in the constructed deformable tensor field, wherein the tangent space is a Riemannian manifold. In the local linear approximation space at the reference point, the mapping relationship is:

[0017] ;

[0018] in, The square root matrix of the deformation tensor of the reference point;

[0019] The exponential mapping is the inverse operation of the logarithmic mapping, used to transform the predicted tangent space vector. Reducing to the predicted deformation tensor ,in Let q be the tangent space vector at the q-th future time step predicted by the time series model. The mapping relationship for the predicted deformation tensor at the q-th future time is as follows:

[0020] ;

[0021] in, This is for matrix exponentiation operations.

[0022] Optionally, the multivariate autoregressive model described in step S3 is expressed as:

[0023] ;

[0024] in, The current time series tangent space vector, For historical timeline moments tangent space vector; The model order represents the number of historical moments used for prediction, determined by the Akaike Information Criterion. Let be the evolution coefficient matrix of order i, and be a 2×2 real matrix, which describes the linear influence of the historical tangent space vector on the current tangent space vector; The residual vector at the current time step follows a zero-mean Gaussian distribution, representing the random error that the model cannot fit; the evolution coefficient matrix The historical tangent space vector sequence is processed using regularized least squares. The parameters are estimated to obtain n, where n is the total number of historical time series moments.

[0025] The beneficial effects of this invention are as follows:

[0026] In step S2 of this invention, the conversion from discrete displacement information to a continuous strain tensor field is achieved by interpolating the temporal point cloud to a unified spatial index grid and calculating the Green-Lagrange strain tensor for each grid point. This tensor includes circumferential normal strain, longitudinal normal strain, and shear strain, and can completely describe the tensile, compressive, and shear deformation state of any point on the lining surface. This overcomes the one-sidedness of existing technologies that only focus on radial convergence or point cloud distance, and provides more comprehensive strain information for tunnel structural health assessment.

[0027] In step S3 of this invention, the deformed tensor sequence is regarded as a Riemannian manifold. The curve is mapped from the nonlinear space to the tangent space via a logarithmic mapping. In the tangent space, a multivariate autoregressive model is used to capture the evolutionary patterns, and then an exponential mapping is used to restore the tensor to the prediction tensor. This approach respects the inherent geometric structure of the deformed tensor data and avoids the geometric distortion caused by linear interpolation or linear regression of the tensor in Euclidean space. Compared to traditional time series prediction methods (such as linear regression, exponential smoothing, and ordinary vector autoregression), this invention significantly improves prediction accuracy, and is particularly suitable for complex conditions where the strain field exhibits nonlinear evolution.

[0028] The unified spatial index (u,v) grid constructed in step S1 of this invention ensures that data from all time series moments are aligned within the same spatial framework. After independently modeling and predicting each spatial index in step S3, step S4 performs spatial clustering on the out-of-limit areas, which can identify warning segments with continuous deformation and output deformation cloud maps. This design not only preserves the temporal evolution information of each spatial location but also captures the regional continuity of deformation through spatial clustering, providing maintenance personnel with complete warning information from "point" to "area".

[0029] In step S4 of this invention, the confidence interval of the predicted deformation value is calculated based on the residual variance of the multivariate autoregressive model, so that the prediction result includes not only point estimates but also quantified uncertainty information. Compared with existing methods that only output a single predicted value, the output result of this invention has greater value for engineering decision-making. Operation and maintenance personnel can judge the reliability of the early warning based on the confidence interval and take differentiated countermeasures (such as reinforcing areas with high confidence exceeding limits and increasing the monitoring frequency for areas with low confidence).

[0030] Other features and advantages of the invention will be set forth in the description which follows, and will be apparent in part from the description, or may be learned by practicing embodiments of the invention. Detailed Implementation

[0031] Example:

[0032] This embodiment provides a method for monitoring and analyzing the full-cycle deformation of tunnel lining based on time-series point clouds. The method includes steps S1, S2, S3 and S4.

[0033] Step S1: Obtain three-dimensional point cloud data of the tunnel lining surface at multiple time points, register the three-dimensional point cloud data, that is, align the three-dimensional point cloud data from different periods to a unified coordinate system, and generate a gridded lining surface point set with a unified spatial index (u,v) by projecting the registered point cloud data onto a cylindrical surface, where u is the circumferential angle parameter and v is the longitudinal mileage parameter. The gridded lining surface point set defines the spatial sampling position shared by all time points, and its specific implementation is as follows:

[0034] Step S11: Use a 3D laser scanner to collect data once a month for a total of n periods. Using the first period's point cloud as a reference, use the iterative nearest point algorithm to register the point clouds of subsequent periods to the coordinate system of the first period, eliminating coordinate deviations caused by differences in the scanner's installation location.

[0035] Step S12: Approximate the tunnel lining surface as a cylindrical surface and establish a cylindrical coordinate system. For each point in the point cloud, calculate its circumferential angle parameter u and longitudinal mileage parameter v, where:

[0036] u is a circumferential angle parameter, with a value range of [0, 2π), which represents the angular position of the point on the cross-section of the lining. It increases clockwise or counterclockwise with the tunnel arch as 0 radians.

[0037] v is the longitudinal mileage parameter, and its value range is the mileage from the start to the end of the tunnel. It represents the distance of the point along the tunnel axis, with the tunnel start point as 0.

[0038] A fixed sampling step size is set on a unified spatial index (u,v) plane, for example, the circumferential step size Δu = 0.02 rad (about 1.15 degrees) and the longitudinal step size Δv = 0.1 m to form a uniform grid. For each grid point, the three-dimensional spatial coordinates of the node are obtained from the original point cloud at that time using the inverse distance weighted interpolation method. Specifically, with a certain grid point as the center, all point cloud points within the search radius r are used, and the three-dimensional coordinates of the grid point are obtained by weighted average according to the inverse distance between the grid point and the grid point.

[0039] Step S13: Output a gridded set of lining surface points with a unified spatial index (u,v). This set defines the spatial sampling locations shared by all time points, ensuring that data from different time points can be compared within the same spatial framework.

[0040] Step S2: For each time series moment, the original point cloud data is interpolated to each grid point of the gridded lining surface point set to obtain the three-dimensional spatial coordinates of each grid point at that time series moment. Then, the displacement field is calculated based on the three-dimensional spatial coordinates of each grid point at that time series moment and the initial moment. The displacement field includes the displacement vector corresponding to each grid point. The displacement vector represents the spatial position change of the corresponding grid point from the initial moment to the current moment. Based on the displacement field, the Green-Lagrange strain tensor A is calculated for each grid point to construct the deformation tensor field at that time series moment.

[0041] For each grid point, the deformation gradient is calculated using the displacement field of its neighboring nodes. On the spatial index (u,v) parameter plane, the displacement gradient is calculated using the central difference method:

[0042] ;in and Let x and y be the components of the displacement vector in the x and y directions, respectively. Then the deformation gradient is: ;in, It is a 2×2 unit tensor.

[0043] Calculation of Green-Lagrange strain tensor:

[0044] A is a 2×2 symmetric positive definite matrix, called the Green-Lagrange strain tensor, and its specific form is:

[0045] ;in, The circumferential strain represents tensile or compressive deformation along the circumferential direction. The longitudinal normal strain represents the tensile or compressive deformation along the longitudinal direction of the tunnel. The shear strain represents the shear deformation between the circumferential and longitudinal directions.

[0046] Output the deformed tensor field at the current time step, i.e., all grid points. corresponding A set of.

[0047] Step S3: Align the deformed tensor fields obtained in step S2 according to their spatial indices. For each spatial index (u,v), align the corresponding temporal deformed tensor sequence. Viewed as a Riemannian manifold The curve on the curve is used to map each tensor to the tangent space at the initial time step through logarithmic mapping to obtain a tangent space vector sequence. The evolution of this tangent space vector sequence is then fitted based on a multivariate autoregressive model, and finally, the predicted deformable tensor is obtained through exponential mapping. The specific implementation method is as follows:

[0048] For each fixed grid point Perform the following time series analysis independently. For simplicity, denote this position as time [time value missing]. The deformable tensor sequence is .

[0049] Step S31: Establish the mathematical space to which the deformation tensor belongs, providing a theoretical basis for subsequent mappings.

[0050] Riemannian manifold representation: All 2×2 symmetric positive definite matrices form a Riemannian manifold. .

[0051] On this manifold, two deformable tensors and The geodesic distance between them is defined as:

[0052] ;

[0053] in, and For two arbitrary deformation tensors, For matrix logarithm operations, For the trace operation of a matrix, For deformation tensor The square root inverse matrix. This distance metric accurately reflects the nonlinear changes between strain tensors, avoiding the distortion of linear metrics in Euclidean space. This geodesic distance definition will later be used to verify the reasonableness of the prediction results (i.e., the geodesic distance between the predicted tensor and the historical tensor should be within a reasonable range), and it is also the geometric basis for understanding logarithmic and exponential mappings.

[0054] Step S32: Convert the deformed tensor sequence on the Riemannian manifold into a vector sequence in the linear tangent space, so that subsequent time series modeling can be performed in the linear space.

[0055] The tangent space mapping (logarithmic mapping) method is as follows: select the initial time. Deformation tensor As a reference point. For each moment. Through logarithmic mapping Mapping to the tangent space of the reference point yields the tangent space vector:

[0056] ;

[0057] in, Let be the square root matrix of the deformation tensor of the reference point, and let the tangent space be a Riemannian manifold. In the locally linear approximation space at the reference point, the tangent space vector... It belongs to this linear space, which facilitates subsequent time series modeling.

[0058] Output of this step This becomes the input to sub-step S33, transforming the nonlinear time series problem into a linear time series problem, where k=1,…,n.

[0059] Step S33: In the linear space of the tangent space, establish a time series model to capture the deformation evolution law and predict the tangent space vector at future times. The specific implementation method is as follows:

[0060] Tangent space vector sequence Establish a multivariate autoregressive model:

[0061] ;

[0062] in, The current time series tangent space vector, For historical timeline moments tangent space vector; The model order represents the number of historical moments used for prediction, determined by the Akaike Information Criterion. Let be the evolution coefficient matrix of order i, and be a 2×2 real matrix, which describes the linear influence of the historical tangent space vector on the current tangent space vector; The residual vector at the current time step follows a zero-mean Gaussian distribution, representing the random error that the model cannot fit; the evolution coefficient matrix The historical tangent space vector sequence is processed using regularized least squares. The parameters are estimated to obtain n, where n is the total number of historical time series moments.

[0063] Estimating the evolution coefficient matrix using regularized least squares method That is, adding while minimizing the sum of squared residuals The norm penalty term is used to prevent overfitting. After parameter estimation, a matrix with definite coefficients is obtained. Multivariate autoregressive model, i=1,…,m.

[0064] The multivariate autoregressive model obtained from the first-stage estimation (i.e., the determined coefficient matrix) Predict the tangent space vector for future moments. Let the current last moment be... Predict the tangent space vector at the q-th time in the future (q≥1):

[0065] ;

[0066] Among them, when hour, ;

[0067] when When that happens, the predicted value is used for recursion.

[0068] Output of this stage The prediction results in the tangent space cannot be directly used as deformation tensors for engineering purposes. They must be restored to the original tensor space through step S34.

[0069] Step S34: Restore the predicted vectors in the tangent space to deformed tensors on the Riemannian manifold to obtain engineering-usable prediction results. The predicted tangent space vectors are restored to deformed tensors via exponential mapping.

[0070] ;

[0071] The exponential mapping is the inverse operation of the logarithmic mapping, used to transform the predicted tangent space vector. Reducing to the predicted deformation tensor ,in Let q be the tangent space vector at the q-th future time step predicted by the time series model. Let be the predicted deformation tensor at the q-th future time, where This is for matrix exponentiation operations.

[0072] Output of this step Compared with the historical deformation tensor output in step S2 Having the same mathematical form and physical meaning, it can be directly input into step S4 for engineering index calculation and early warning judgment.

[0073] The output is for each spatial index Predicted deformation tensor .

[0074] Step S4: Based on the predicted deformation tensor Calculate the engineering deformation index, compare the engineering deformation index with a preset threshold, perform spatial clustering on spatial indices that exceed the preset threshold, and output deformation warning areas and predicted deformation values, including:

[0075] Based on the predicted deformation tensor Commonly used engineering deformation indices are used to calculate the various elements. (Note: The original text contains some inconsistencies and unclear The tensor elements are:

[0076] ;

[0077] ;

[0078] ;

[0079] The circumferential strain represents tensile or compressive deformation along the circumferential direction. The longitudinal normal strain represents the tensile or compressive deformation along the longitudinal direction of the tunnel. Shear strain represents the shear deformation between the circumferential and longitudinal directions. The principal strain is the circumferential strain, representing the maximum tensile or compressive strain in the circumferential direction of the lining. The longitudinal principal strain represents the maximum tensile or compressive strain in the longitudinal direction of the lining. The maximum shear strain represents the degree of shear deformation of the lining.

[0080] For grid nodes exceeding any preset threshold Spatial clustering is performed. A density-based spatial clustering algorithm is used to merge adjacent out-of-limit nodes into continuous regions, with each region corresponding to a deformation warning segment.

[0081] Based on the residual variance of the multivariate autoregressive model in step S3, calculate the confidence interval of the predicted values. Let the residual vector be... If the covariance matrix is ​​Σ, then the covariance matrix of the predicted tangent space vector can be obtained by linear recursion propagation. Then, the covariance is propagated to the deformed tensor space by the differential approximation of the exponential mapping (first-order Taylor expansion) to obtain the confidence interval of each element of the predicted deformed tensor.

[0082] Output the following data:

[0083] The predicted strain values ​​(such as circumferential principal strain) of each region are displayed using color codes on the tunnel development diagram.

[0084] Warning zone mileage range: The longitudinal mileage start and end range and circumferential angle range corresponding to each cluster region are output in tabular form as the predicted strain value and its 95% confidence interval for each warning zone.

[0085] The implementation principle of this embodiment can be summarized into three core steps: "tensor field construction under a unified spatial benchmark, nonlinear temporal mapping on a Riemannian manifold, and early warning output driven by engineering indicators." These steps are described in detail below.

[0086] Tensor Field Construction under a Unified Spatial Reference: The point clouds from different tunnel scanning phases exist in different local coordinate systems, and their density and distribution vary. First, registration transforms all point clouds to the initial coordinate system. Then, cylindrical projection maps the 3D point clouds onto a 2D parametric plane composed of the circumferential angle *u* and the longitudinal mileage *v*. A uniform grid with a fixed step size is set on this plane, and spatial interpolation is used to assign 3D coordinates to each grid node. Thus, point cloud data at all times are expressed on the same set of spatial index (u,v) grid points, laying a spatial reference for subsequent point-by-point comparisons. Based on this, for each time step, the displacement field is obtained by subtracting the current grid point coordinates from the initial coordinates. The gradient of the displacement field is then used to calculate the Green-Lagrange strain tensor. This tensor is a 2×2 symmetric positive definite matrix, where the diagonal elements represent the circumferential and longitudinal normal strains, and the off-diagonal elements represent the shear strain. Repeated calculations are performed for each grid point to obtain the deformation tensor field at that time step. Thus, the original discrete point cloud is transformed into a spatially aligned strain tensor sequence with clear physical meaning.

[0087] Nonlinear Temporal Mapping on Riemannian Manifolds: Green-Lagrange strain tensors are symmetric positive definite matrices, and their entirety constitutes a Riemannian manifold, i.e., a nonlinear space. Traditional temporal models (such as vector autoregression) are only applicable to linear Euclidean spaces. Directly modeling the tensor elements linearly would violate the geometric constraints within the tensor and introduce distortion. Therefore, this invention introduces a manifold learning strategy: First, the tensor at the initial time step is selected as the reference point. A logarithmic mapping is used to map the tensors at subsequent time steps from the Riemannian manifold to the tangent space at the reference point. The tangent space is a linear space, and the mapped vectors retain the geodesic distance information between the original tensors and satisfy linear operation rules. In the tangent space, a multivariate autoregressive model is established for the tangent space vector sequence at each spatial location. The model order is determined using the Akaike information criterion, and the evolution coefficient matrix is ​​estimated using regularized least squares. This model can capture the linear evolution law of the tangent space vectors. The estimated model is then used to recursively extrapolate forward to obtain the predicted tangent space vectors for future time steps. Finally, the predicted tangent space vector is restored to a deformed tensor on the Riemannian manifold through an exponential mapping (the inverse operation of the logarithmic mapping). The entire process achieves a complete mapping from nonlinear to linear to nonlinear, completing the prediction of future strain states while respecting the tensor's geometry.

[0088] Engineering-driven early warning output: The predicted deformation tensor includes circumferential normal strain, longitudinal normal strain, and shear strain. Based on the formulas of elasticity, the circumferential principal strain, longitudinal principal strain, and maximum shear strain can be calculated from these tensor elements. These indicators directly correspond to the deformation limits in the tunnel structure design code. The predicted indicators of each grid point are compared with dynamically set thresholds (determined by combining the code and historical data) to identify grid points exceeding the limits. A spatial clustering algorithm is then used to merge adjacent exceeding-limit points into continuous early warning sections. Simultaneously, based on the residual variance of the autoregressive model, the confidence interval of the predicted values ​​can be calculated, providing uncertainty quantification for decision-making. The final output includes a deformation cloud map, the mileage range of the early warning section, and the predicted deformation values ​​with confidence intervals, providing maintenance personnel with information to formulate inspection or reinforcement plans.

[0089] In step S2 of this embodiment, the conversion from discrete displacement information to a continuous strain tensor field is achieved by interpolating the temporal point cloud to a unified spatial index grid and calculating the Green-Lagrange strain tensor for each grid point. This tensor includes circumferential normal strain, longitudinal normal strain, and shear strain, and can completely describe the tensile, compressive, and shear deformation state of any point on the lining surface. This overcomes the one-sidedness of existing technologies that only focus on radial convergence or point cloud distance, and provides more comprehensive strain information for tunnel structural health assessment.

[0090] In step S3 of this embodiment, the deformable tensor sequence is regarded as a Riemannian manifold. The curve is mapped from the nonlinear space to the tangent space via a logarithmic mapping. In the tangent space, a multivariate autoregressive model is used to capture the evolutionary patterns, and then an exponential mapping is used to restore the tensor to the prediction tensor. This approach respects the inherent geometric structure of the deformed tensor data and avoids the geometric distortion caused by linear interpolation or linear regression of the tensor in Euclidean space. Compared to traditional time series prediction methods (such as linear regression, exponential smoothing, and ordinary vector autoregression), this invention significantly improves prediction accuracy, and is particularly suitable for complex conditions where the strain field exhibits nonlinear evolution.

[0091] In this embodiment, the unified spatial index (u,v) grid constructed in step S1 ensures that data from all time series moments are aligned within the same spatial framework. After independently modeling and predicting each spatial index in step S3, step S4 performs spatial clustering on the out-of-limit areas, which can identify warning segments with continuous deformation and output deformation cloud maps. This design not only preserves the temporal evolution information of each spatial location but also captures the regional continuity of deformation through spatial clustering, providing maintenance personnel with complete warning information from "point" to "area".

[0092] In step S4 of this embodiment, the confidence interval of the predicted deformation value is calculated based on the residual variance of the multivariate autoregressive model, so that the prediction result includes not only point estimates but also quantified uncertainty information. Compared with existing methods that only output a single predicted value, the output result of this invention has greater value for engineering decision-making. Operation and maintenance personnel can judge the reliability of the early warning based on the confidence interval and take differentiated countermeasures (such as reinforcing areas with high confidence exceeding limits and increasing the monitoring frequency for areas with low confidence).

[0093] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for monitoring and analyzing the full-cycle deformation of tunnel lining based on time-series point clouds, characterized in that, The method includes: Step S1: Obtain three-dimensional point cloud data of the tunnel lining surface at multiple time series moments, register the three-dimensional point cloud data, and generate a gridded lining surface point set with a unified spatial index (u,v) by projecting the registered point cloud data onto a cylindrical surface, where u is the circumferential angle parameter and v is the longitudinal mileage parameter. The gridded lining surface point set defines the spatial sampling position shared by all time series moments. Step S2: For each time series moment, the original point cloud data is interpolated to each grid point of the gridded lining surface point set to obtain the three-dimensional spatial coordinates of each grid point at that time series moment. Then, the displacement field is calculated based on the three-dimensional spatial coordinates of each grid point at that time series moment and the initial time. Based on the displacement field, the Green-Lagrange strain tensor A is calculated for each grid point to construct the deformation tensor field at that time series moment. Step S3: Align the deformed tensor fields obtained in step S2 according to their spatial indices. For each spatial index (u,v), align the corresponding temporal deformed tensor sequence. Viewed as a Riemannian manifold The curve on the curve is used to map each tensor to the tangent space at the initial time step through logarithmic mapping to obtain a tangent space vector sequence. The evolution of this tangent space vector sequence is then fitted based on a multivariate autoregressive model, and finally, the predicted deformable tensor is obtained through exponential mapping. ; Step S4: Based on the predicted deformation tensor Calculate the engineering deformation index, compare the engineering deformation index with a preset threshold, perform spatial clustering on spatial indices that exceed the preset threshold, and output the deformation warning area and predicted deformation value.

2. The method for monitoring and analyzing the full-cycle deformation of tunnel lining based on time-series point clouds according to claim 1, characterized in that, The Green-Lagrange strain tensor is defined as follows: ,in For deformation gradient, For unit tensors, It is a 2×2 symmetric positive definite matrix, whose tensor elements include circumferential normal strain, longitudinal normal strain and shear strain.

3. The method for monitoring and analyzing the full-cycle deformation of tunnel lining based on time-series point clouds according to claim 2, characterized in that, The logarithmic mapping and exponential mapping described in step S3 are both based on the geodesic distance between tensors, and the specific implementation method is as follows: Define geodesic distance for measuring Riemannian manifolds The difference between the two deformation tensors, the Riemannian manifold Let the space be the space formed by all 2×2 symmetric positive definite matrices; For any two deformable tensors and Its geodetic distance is: ； in, and For two arbitrary deformation tensors, For matrix logarithm operations, For the trace operation of a matrix, For deformation tensor The square root inverse matrix; With the initial deformation tensor As a reference point, the initial deformation tensor This refers to the deformable tensor corresponding to the spatial index in the deformable tensor field constructed at the first time step in step S2; Logarithmic mapping transforms the tensor at any given time step. Mapping to the tangent space of the reference point yields the tangent space vector. ,in For step S2 at the timing time The deformable tensor corresponding to the spatial index in the constructed deformable tensor field, wherein the tangent space is a Riemannian manifold. In the local linear approximation space at the reference point, the mapping relationship is: ； in, The square root matrix of the deformation tensor of the reference point; The exponential mapping is the inverse operation of the logarithmic mapping, used to transform the predicted tangent space vector. Reducing to the predicted deformation tensor ,in Let q be the tangent space vector at the q-th future time step predicted by the time series model. The mapping relationship for the predicted deformation tensor at the q-th future time is as follows: ； in, This is for matrix exponentiation operations.

4. The method for monitoring and analyzing the full-cycle deformation of tunnel lining based on time-series point clouds according to claim 3, characterized in that, The multivariate autoregressive model described in step S3 is expressed as follows: ； in, The current time series tangent space vector, For historical timeline moments tangent space vector; The model order represents the number of historical moments used for prediction, determined by the Akaike Information Criterion. Let be the evolution coefficient matrix of order i, and be a 2×2 real matrix, which describes the linear influence of the historical tangent space vector on the current tangent space vector; The residual vector at the current time step follows a zero-mean Gaussian distribution, representing the random error that the model cannot fit; the evolution coefficient matrix The historical tangent space vector sequence is processed using regularized least squares. The parameters are estimated to obtain n, where n is the total number of historical time series moments.

Images