A surrounding rock internal strain field inversion method and system based on strain modal reconstruction

Abstract

The application discloses a kind of based on strain modal reconstruction's surrounding rock internal strain field inversion method and system, it is related to geotechnical engineering monitoring and inversion analysis technical field.The method first constructs surrounding rock three-dimensional calculation domain and space coordinate system, acquires distributed optical fiber along line multiple measuring point strain data and strain gage point strain data, and it is preprocessed and time benchmark unification;Subsequently, establish the spatial topological mapping relationship between distributed optical fiber along line observation point, strain gage observation point and three-dimensional calculation domain, form observation point set and measured strain vector;On this basis, construct strain modal mode shape library, extract the modal value at observation point and form observation modal matrix, establish the transfer relationship between measured strain vector and modal coordinates;Finally, introduce regularized constraint to solve modal coordinates, and reconstruct the internal strain field of surrounding rock.The application can realize the stable reconstruction of the internal strain field of surrounding rock, and provide data basis for surrounding rock local deformation identification and damage evolution analysis.

Description

Technical Field

[0001] This invention relates to the field of geotechnical engineering monitoring and inversion analysis technology, and in particular to a method and system for inverting the internal strain field of surrounding rock based on strain mode reconstruction. Background Technology

[0002] Surrounding rock undergoes complex deformation responses during mining disturbances, dynamic-static load coupling, or underground engineering excavation. Its internal strain distribution can reflect local deformation, damage propagation, and potential instability processes. Obtaining the internal strain field of the surrounding rock is crucial for analyzing its deformation evolution and identifying local anomaly areas. However, the internal deformation of surrounding rock typically exhibits spatial non-uniformity and temporal variation, making it difficult to directly obtain the strain field distribution within the monitored area using strain data from only a limited number of measuring points.

[0003] Currently, surrounding rock strain monitoring commonly employs methods such as resistance strain gauges, fiber Bragg grating sensors, and distributed fiber optic sensing technology. Strain gauges can acquire local strain responses at specific measuring points; distributed fiber optic sensing technology can acquire strain data from multiple measuring points along the fiber optic path, reflecting strain variation characteristics near the fiber optic path. While these methods provide effective data sources for surrounding rock deformation monitoring, the monitoring results are inherently limited by the sensor deployment location and spatial coverage, typically presenting as point-based or distributed observation data along a line, and cannot be directly equated to a continuous strain field within the surrounding rock.

[0004] In practical engineering or physical model tests, the number, deployment path, and coverage of strain gauges and fiber optic sensors are usually limited due to sensor installation conditions, the complexity of the surrounding rock medium, and monitoring space constraints. For the strain field inside the surrounding rock that needs to be inverted, the number of spatial nodes to be determined is often greater than the number of effective observation data that can be obtained. Directly reconstructing the strain field from limited monitoring data can easily lead to instability in the inversion. If only conventional spatial interpolation, empirical fitting, or ordinary least squares methods are used for strain field estimation, the inversion results may be affected by the measurement point layout, data noise, and local outliers, resulting in problems such as local oscillations, unreasonable spatial distribution, or insufficient characterization of key deformation areas.

[0005] Therefore, there is an urgent need for a method and system for inverting the internal strain field of surrounding rock based on strain mode reconstruction that can solve the above problems. Summary of the Invention

[0006] This solution addresses the problems and needs raised above by proposing a method and system for inverting the internal strain field of surrounding rock based on strain mode reconstruction. The above technical objectives can be achieved by adopting the following technical features, and it also brings several other technical benefits.

[0007] One objective of this invention is to propose a method for inverting the strain field inside surrounding rock based on strain mode reconstruction, comprising the following steps: S10: Based on the geometry of the surrounding rock of the roadway to be monitored or the physical model sample, the monitoring range, and the sensor deployment area, determine the three-dimensional computational domain for strain field inversion, establish a unified three-dimensional global coordinate system O-XYZ, and spatially discretize the three-dimensional computational domain to form a set of grid nodes N. m ; S20: Collect distributed fiber optic strain data from multiple measuring points obtained by distributed fiber optic sensors along the fiber optic deployment path, as well as point strain data obtained by strain gauges at key measuring points, and form an original strain monitoring data set from the distributed fiber optic strain data and strain gauge strain data. S30: Preprocess the distributed fiber strain data and strain gauge strain data to obtain standardized strain observation data under the same time series; S40: Map the observation points along the distributed optical fiber and the strain gauge observation points to the established three-dimensional computational domain in order to establish the correspondence between strain observation data and spatial location, and obtain the set of observation points and the measured strain vector. S50: Based on a three-dimensional computational domain and mesh node set N m Construct all strain mode shapes used to characterize the spatial distribution of strain field inside the surrounding rock, and form a strain mode shape library; S60: Based on the set of observation points, extract the mode shape values ​​at each observation point location from the strain mode shape library, construct the observation mode matrix, and establish the transfer relationship between the measured strain vector and the modal coordinates; S70: Construct a regularized inversion objective function, solve for the optimal modal coordinates corresponding to each inversion time, reconstruct the internal strain field of the surrounding rock based on the strain mode shape library and the optimal modal coordinates, and output the inversion results.

[0008] Furthermore, the method for inverting the internal strain field of surrounding rock based on strain mode reconstruction according to the present invention may also have the following technical features: In one example of the present invention, step S10 specifically includes the following steps: S11: Assume the region to be inverted within the surrounding rock is a three-dimensional computational domain:

[0009] In the formula, Ω represents the spatial region within the surrounding rock to be inverted. Represents three-dimensional space; S12: Within the three-dimensional computational domain, any spatial location is represented as:

[0010] In the formula, Let x, y, and z be the spatial position vectors, where x, y, and z are the coordinates of a point in space in the X, Y, and Z directions, respectively, and T represents the transpose. S13: For any time t, the strain field inside the surrounding rock to be inverted is composed of the strain values ​​at various spatial locations within the three-dimensional computational domain, and is expressed as:

[0011] In the formula, ε(x,t) represents the value of the strain field inside the surrounding rock at spatial location x and time t; S14: Spatial discretization of the three-dimensional computational domain is performed to form multiple mesh nodes or spatial units; if node discretization is used, a set of mesh nodes is obtained:

[0012] In the formula, N m x represents the set of grid nodes within the computational domain. a Let represent the spatial coordinates of the a-th grid node, and n represent the total number of grid nodes.

[0013] In one example of the present invention, step S20 specifically includes the following steps: Distributed fiber optic sensors are deployed in the surrounding rock of the roadway to be monitored or in physical model samples. These sensors are deployed along the roadway perimeter, radially, circumferentially, along the roof and floor directions, or other predetermined paths to acquire strain data from multiple observation points distributed along the fiber optic deployment path. The distributed fiber optic strain data acquired by the distributed fiber optic sensors is expressed as follows:

[0014] In the formula, ε f (s i ,t j ) represents the observation point s along the distributed optical fiber. i At time t j The collected strain values, s i Let t represent the i-th observation point along the distributed optical fiber. j This represents the j-th sampling time. Simultaneously, strain gauges are installed on the roof, floor, sidewalls, shoulder corners, or other locations sensitive to local deformation in the roadway to obtain strain data at key locations; the strain data obtained from the strain gauges is expressed as follows:

[0015] In the formula, ε g (p k ,t j ) indicates the strain gauge observation point p k At time t jThe collected strain value, p k This represents the observation point of the k-th strain gauge; The raw strain data acquired by distributed fiber optic sensors and strain gauges constitute the raw monitoring data set E0:

[0016] In the formula, E0 represents the set of original strain monitoring data used for strain field inversion.

[0017] In one example of the present invention, step S30 specifically includes the following steps: S31: Perform outlier removal, noise filtering, baseline correction, and unit unification on the strain data in the original monitoring data set E0. For distributed fiber optic strain data, outliers are identified based on the strain change amplitude of adjacent observation points. For strain gauge strain data, outliers are identified based on the historical response range of the measurement point or the rate of change at adjacent times. Unify distributed fiber optic strain data and strain gauge strain data into a common time series:

[0018] In the formula, T represents the unified time series used for strain field inversion, and t j Let j represent the j-th inversion time, and m represent the total number of inversion times; S32: After preprocessing and time unification, at any time t j The following is a standardized strain observation data set:

[0019] Among them, E m (t j ) represents time t j The standardized strain observation data set that participates in strain field inversion, ε f (s i ,t j ) represents the observation point s along the distributed optical fiber. i The strain observation value at ε g (p k ,t j ) indicates the strain gauge observation point p k Strain observations at the location.

[0020] In one example of the present invention, step S40 specifically includes the following steps: S41: For distributed fiber strain data, the original observation points are represented by the distance along the distributed fiber. Therefore, a mapping relationship between the observation points along the distributed fiber and the three-dimensional spatial coordinates is established, assuming the fiber path function is:

[0021] In the formula, s represents the observation point along the distributed optical fiber, r(s) represents the spatial position function of the optical fiber path in the three-dimensional computational domain, and x represents the three-dimensional spatial coordinates corresponding to the observation point along the distributed optical fiber. For the i-th observation point s along the distributed optical fiber... i Its corresponding three-dimensional spatial coordinates are represented as:

[0022] In the formula, This represents the spatial location of the observation point along the distributed optical fiber in the three-dimensional global coordinate system O-XYZ; thus, the distributed optical fiber strain data ε f (s i ,t j Converted to strain observation values ​​ε at a three-dimensional spatial location f (x i ,t j ); S42: For strain gauge strain data, determine the three-dimensional spatial coordinates of the k-th strain gauge observation point based on the actual placement of the strain gauges in the surrounding rock of the tunnel or the physical model sample:

[0023] In the formula, x k Indicates the strain gauge observation point p k Spatial position in the three-dimensional global coordinate system; thus, strain gauge strain data ε g (p k ,t j ) represents the spatial location x k Strain observation ε at the location g (x k ,t j ); S43: Organize the observation points along the distributed optical fiber and strain gauge observation points into a unified observation point set:

[0024] In the formula, P represents the set of observation points participating in the strain field inversion, and x h Let H represent the spatial coordinates of the h-th observation point, and M represent the total number of observation points. S44: At any inversion time t j Next, based on the set of observation points P and their corresponding strain observation values, the measured strain vector is constructed:

[0025] In the formula, ε m (t j ) represents time t jThe measured strain vector ε participating in the inversion h (t j ) indicates that the h-th observation point is at time t j The strain observation values.

[0026] In one example of the present invention, step S50 specifically includes the following steps: S51: For any spatial location x and time t, the strain values ​​of the internal strain field of the surrounding rock at that spatial location and time can be expressed as a linear combination of the Nth order strain mode shape and the modal coordinates:

[0027] In the formula, ε(x,t) represents the strain value at spatial location x at time t; q represents the value of the r-th strain mode at position x; r (t) represents the modal coordinates of the r-th strain mode at time t; N represents the order of the strain modes involved in the reconstruction; S52: Store the obtained strain mode shapes according to the same three-dimensional computational domain and mesh node order to form a strain mode shape library:

[0028] In the formula, Φ represents the strain mode shape library. This represents the set of values ​​for the r-th strain mode at each grid node within the computational domain.

[0029] In one example of the present invention, step S60 specifically includes the following steps: S61: Based on the set of observation points, extract the mode shape values ​​corresponding to each observation point from the constructed strain mode shape library Φ; for the h-th observation point x h The corresponding modal values ​​are expressed as follows:

[0030] In the formula, x h Represents the spatial coordinates of the h-th observation point. This represents the value of the r-th strain mode at the observation point, and N represents the order of the modes involved in the reconstruction. S62: Arrange the modal values ​​at all observation points in the order of observation points to construct the observation modal matrix:

[0031] In the formula, K represents the observation mode matrix, the rows of the matrix correspond to the observation points along the distributed optical fiber or the observation points of the strain gauge, and the columns of the matrix correspond to different strain modes. S63: At any inversion time t jBelow, based on the constructed measured strain vector ε m (t j Based on the observed modal matrix K, establish the transfer equation between the measured strain vector and the modal coordinates:

[0032] In the formula, ε m (t j ) represents time t j The measured strain vector below is composed of observation points along the distributed optical fiber and strain gauge observation points; q(t) j ) represents the modal coordinate vector to be solved; η(t) j ) indicates measurement noise or model error.

[0033] In one example of the present invention, step S70 specifically includes the following steps: S71: Using the deviation between the measured strain vector and the calculated strain vector as the data fitting term, and introducing a regularization constraint term, an objective function is constructed to solve for the modal coordinates:

[0034] In the formula, J(q) represents the objective function to be optimized; K represents the observed mode matrix; q(t) represents the objective function to be optimized; K represents the observed mode matrix; and q(t) represents the objective function to be optimized. j ) represents time t j The modal coordinate vector to be solved; ε m (t j ) represents time t j The measured strain vector is given by λ, where λ represents the regularization parameter and R(q) represents the regularization constraint term. S72: Optimize the objective function to obtain time t. j The optimal modal coordinate vector is as follows:

[0035] In the formula, Represents time t j The modal coordinate vector that minimizes the objective function; S73: Obtain the optimal modal coordinates Substituting into the established strain modal expression, we obtain time t. j Inversion strain value at any spatial location x inside the surrounding rock:

[0036] In the formula, Indicates spatial position x at time t j The inversion strain value; This represents the value of the r-th strain mode at position x; This indicates that the r-th mode occurs at time t.j The optimal modal coordinates are given; N represents the modal order involved in the reconstruction. S74: For each grid node in the three-dimensional computational domain, calculate its corresponding inversion strain value, and form the time t based on the inversion strain value on the grid node. j Reconstruction results of the strain field inside the surrounding rock:

[0037] In the formula, This represents the inversion result of the continuous strain field within the three-dimensional computational domain; where, if it is necessary to analyze the dynamic evolution process of the surrounding rock strain field, then a unified time series T={t1, t2, ..., t...} is used. m Repeat the continuous strain field inversion calculation at each inversion time point in the formula to obtain the continuous strain field sequence inside the surrounding rock: .

[0038] S75: Calculate the strain gradient, local maximum strain value and its spatial location based on the continuous strain field obtained by inversion, and identify strain concentration areas or strain localization zones inside the surrounding rock.

[0039] In one example of the present invention, after step S75, the method further includes: selecting observation points or strain gauge observation points along the distributed optical fiber that did not participate in the modal coordinate solution as verification points, and calculating the difference between the inverted strain value and the measured strain value at the verification point to evaluate the strain field inversion error. The error expression is as follows:

[0040] In the formula, e h (t j ) indicates that the h-th verification point is at time t. j Inversion error; This represents the inversion strain value at the verification point; ε h obs (t j ) represents the measured strain value at the verification point.

[0041] Another objective of this invention is to propose a system for inverting the strain field inside surrounding rock based on strain mode reconstruction, comprising: The unified coordinate module is configured to determine the three-dimensional computational domain for strain field inversion based on the geometry, monitoring range, and sensor deployment area of ​​the surrounding rock or physical model sample of the roadway to be monitored. It establishes a unified three-dimensional global coordinate system O-XYZ and spatially discretizes the three-dimensional computational domain to form a set of grid nodes N. m ; The data set module is configured to collect distributed fiber strain data from multiple measuring points obtained by distributed fiber optic sensors along the fiber optic deployment path, as well as point strain data obtained by strain gauges at key measuring points, and to form an original strain monitoring data set from the distributed fiber optic strain data and the strain gauge strain data. The data preprocessing module is configured to preprocess distributed fiber strain data and strain gauge strain data to obtain standardized strain observation data under the same time series. The correspondence establishment module is configured to uniformly map the observation points along the distributed optical fiber and the strain gauge observation points to the established three-dimensional computing domain, so as to establish the correspondence between strain observation data and spatial location, and obtain the set of observation points and the measured strain vector. The modal shape library module is configured based on a three-dimensional computational domain and a set of mesh nodes N. m Construct all strain mode shapes used to characterize the spatial distribution of strain field inside the surrounding rock, and form a strain mode shape library; The modal shape value module is configured to extract the modal shape values ​​at each observation point from the strain modal shape library after obtaining the strain modal shape library, construct the observation modal matrix, and establish the transfer relationship between the measured strain vector and the modal coordinates. The inversion result output module is configured to construct a regularized inversion objective function, solve for the optimal modal coordinates corresponding to each inversion time, reconstruct the internal strain field of the surrounding rock based on the strain mode mode library and the optimal modal coordinates, and output the inversion results.

[0042] Compared with the prior art, the present invention has the following beneficial effects: (1) This invention uses multi-point strain data acquired along the fiber path of a distributed optical fiber and point strain data from strain gauges as inversion inputs. The distributed optical fiber data reflects the strain variation characteristics near the fiber path, while the strain gauge data provides local strain observation results at key locations. The combination of the two provides a relatively complete observation data foundation for strain field inversion within the surrounding rock, even with a limited number of sensors.

[0043] (2) This invention establishes a spatial topological mapping relationship between the coordinates along the distributed optical fiber, the observation points of the strain gauges, and the three-dimensional computational domain, thereby uniformly transforming strain data collected by different types of sensors into the same spatial coordinate system and forming a set of observation points and a measured strain vector. This processing method can reduce the inconsistency in the spatial representation of data from different sensors, enabling distributed strain data along the fiber and point strain data to participate in subsequent inversion calculations.

[0044] (3) Based on the concept of strain mode reconstruction, this invention represents the continuous strain field inside the surrounding rock as a combination of finite-order strain mode shapes and modal coordinates, and extracts the modal values ​​at the observation locations from the strain mode shape library according to the set of observation points to construct the observation mode matrix. Compared with directly inverting the strain values ​​of all spatial grid nodes, this method can reduce the number of unknowns to be solved and reduce the difficulty of solving the inversion problem under the condition of limited observation data.

[0045] (4) Based on the transfer relationship between the measured strain vector and modal coordinates, this invention introduces regularization constraints to construct the inversion objective function and solves for the modal coordinates. This method can reduce the impact of ill-conditioned observation modal matrix, monitoring noise, and local outliers on the inversion results to a certain extent, so that the reconstructed strain field can meet the fitting requirements of the observation data while maintaining good spatial continuity and stability. Based on the continuous strain field obtained by inversion, strain cloud maps, strain gradient fields, and strain localization zones can be further obtained, providing a reference for the analysis of surrounding rock damage evolution and the identification of local deformation.

[0046] The preferred embodiments of the invention will be described in more detail below with reference to the accompanying drawings, so as to facilitate an understanding of the features and advantages of the invention. Attached Figure Description

[0047] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings of the embodiments of the present invention will be briefly described below. The drawings are merely illustrative of some embodiments of the present invention and are not intended to limit the scope of the present invention to all embodiments.

[0048] Figure 1 This is a flowchart of the method for inverting the internal strain field of surrounding rock based on strain mode reconstruction according to an embodiment of the present invention; Figure 2 This is a schematic diagram of the three-dimensional computational domain, disturbance input location, distributed optical fiber, and strain gauge layout according to an embodiment of the present invention; Figure 3 This is a schematic diagram illustrating the mapping of sensor measurement points to a three-dimensional computational domain according to an embodiment of the present invention; Figure 4 This is a schematic diagram illustrating the strain mode reconstruction and regularization inversion principle according to an embodiment of the present invention. Detailed Implementation

[0049] To make the objectives, technical solutions, and advantages of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. The same reference numerals in the drawings represent the same components. It should be noted that the described embodiments are only some, not all, of the embodiments of the present invention. All other embodiments obtained by those skilled in the art based on the described embodiments of the present invention without creative effort are within the scope of protection of the present invention.

[0050] According to a first aspect of the present invention, a method for inverting the internal strain field of surrounding rock based on strain mode reconstruction is provided, such as... Figure 1 As shown, it includes the following steps: S10: Based on the geometry of the surrounding rock of the roadway to be monitored or the physical model sample, the monitoring range, and the sensor deployment area, determine the three-dimensional computational domain for strain field inversion, establish a unified three-dimensional global coordinate system O-XYZ, and spatially discretize the three-dimensional computational domain to form a set of grid nodes N. m ; S20: Collect distributed fiber optic strain data from multiple measuring points obtained by distributed fiber optic sensors along the fiber optic deployment path, as well as point strain data obtained by strain gauges at key measuring points, and form an original strain monitoring data set from the distributed fiber optic strain data and strain gauge strain data. S30: Preprocess the distributed fiber strain data and strain gauge strain data to obtain standardized strain observation data under the same time series; S40: Establish the spatial topological mapping relationship between distributed optical fibers and strain gauges, and construct the measured strain vector: After obtaining standardized strain observation data under a unified time reference, the observation points along the distributed optical fiber and the observation points of the strain gauges are uniformly mapped to the established three-dimensional computing domain to establish the correspondence between strain observation data and spatial location, and obtain the set of observation points and the measured strain vector. S50: Constructing a strain mode library for reconstructing continuous strain fields within surrounding rock: based on a three-dimensional computational domain and a mesh node set N m We construct all strain mode shapes used to characterize the spatial distribution of strain field inside the surrounding rock and form a strain mode shape library. By representing the continuous strain field as a combination of finite-order strain modes, we can reduce the number of unknowns caused by directly inverting the strain values ​​of all grid nodes and improve the stability of subsequent solutions.

[0051] S60: After obtaining the strain mode shape library, extract the mode shape values ​​at each observation point location from the strain mode shape library according to the set of observation points, construct the observation mode matrix, and establish the transfer relationship between the measured strain vector and the modal coordinates; S70: Construct a regularized inversion objective function, solve for the optimal modal coordinates corresponding to each inversion time, reconstruct the internal strain field of the surrounding rock based on the strain mode shape library and the optimal modal coordinates, and output the inversion results.

[0052] This method uses multi-point strain data acquired along the fiber path of a distributed optical fiber, along with point-based strain data from strain gauges, as inputs for inversion. The distributed optical fiber data reflects strain variation characteristics near the fiber's path, while the strain gauge data provides local strain observation results at key locations. Combining these two methods provides a relatively complete observational data foundation for inverting the strain field within the surrounding rock, even with a limited number of sensors deployed.

[0053] This method establishes a spatial topological mapping relationship between distributed fiber optic coordinates, strain gauge observation points, and a three-dimensional computational domain. This transforms strain data collected by different types of sensors into a unified spatial coordinate system, forming a set of observation points and a measured strain vector. This processing reduces the inconsistency in spatial representation of data from different sensors, enabling distributed strain data and point-based strain data to participate together in subsequent inversion calculations.

[0054] This method, based on the concept of strain mode reconstruction, represents the continuous strain field inside the surrounding rock as a combination of finite-order strain mode shapes and modal coordinates. It then extracts the modal values ​​at the observation locations from a strain mode shape library based on the set of observation points, constructing an observation mode matrix. Compared to directly inverting the strain values ​​of all spatial grid nodes, this method reduces the number of unknowns and lowers the difficulty of solving the inversion problem under limited observation data.

[0055] This method, based on the transfer relationship between measured strain vectors and modal coordinates, introduces regularization constraints to construct an inversion objective function and solves for the modal coordinates. This method can, to a certain extent, reduce the impact of ill-conditioned observation modal matrix, monitoring noise, and local outliers on the inversion results, ensuring that the reconstructed strain field maintains good spatial continuity and stability while meeting the requirements for fitting observation data. Based on the continuous strain field obtained through inversion, strain contour maps, strain gradient fields, and strain localization zones can be further obtained, providing a reference for surrounding rock damage evolution analysis and local deformation identification.

[0056] In one example of the present invention, step S10 specifically includes the following steps: S11: Assume the region to be inverted within the surrounding rock is a three-dimensional computational domain:

[0057] In the formula, Ω represents the spatial region within the surrounding rock to be inverted. The three-dimensional computational domain represents three-dimensional space. For the surrounding rock of an engineering tunnel, the three-dimensional computational domain can be selected as the surrounding rock area within a certain depth range around the tunnel. For physical model tests, the three-dimensional computational domain can be selected as the internal area of ​​the sample containing the tunnel model and its surrounding rock. S12: Within the three-dimensional computational domain, any spatial location is represented as:

[0058] In the formula, Let x, y, and z be the spatial position vectors, where x, y, and z are the coordinates of a point in space in the X, Y, and Z directions, respectively, and T represents the transpose. S13: For any time t, the strain field inside the surrounding rock to be inverted is composed of the strain values ​​at various spatial locations within the three-dimensional computational domain, and is expressed as:

[0059] In the formula, ε(x,t) represents the value of the strain field inside the surrounding rock at spatial location x and time t; the strain value can be a single component strain along the fiber direction, the roadway radial direction, the vertical direction, the tangential direction, or the principal strain direction; when multi-component strain inversion is required, it can also be extended to a strain vector containing multiple strain components.

[0060] S14: Spatial discretization of the three-dimensional computational domain is performed to form several mesh nodes or spatial elements; if node discretization is used, a set of mesh nodes is obtained:

[0061] In the formula, N m x represents the set of grid nodes within the computational domain. a This represents the spatial coordinates of the a-th grid node, and n represents the total number of grid nodes. The subsequent inversion of the continuous strain field can be calculated, interpolated, and visualized on the above nodes or elements.

[0062] In one example of the present invention, such as Figure 2 As shown, step S20 specifically includes the following steps: Distributed fiber optic sensors are deployed in the surrounding rock of the roadway to be monitored or in physical model samples. These sensors are deployed along the roadway perimeter, radially, circumferentially, along the roof and floor directions, or other predetermined paths to acquire multi-point strain data distributed along the fiber optic deployment path. The distributed fiber optic strain data acquired by the distributed fiber optic sensors is expressed as follows:

[0063] In the formula, ε f (s i ,t j ) represents the observation point s along the distributed optical fiber.i At time t j The collected strain values, s i Let t represent the i-th observation point along the distributed optical fiber. j This represents the j-th sampling time. Simultaneously, strain gauges are installed on the roof, floor, sidewalls, shoulder corners, or other locations sensitive to local deformation in the roadway to obtain strain data at key locations; the strain data obtained from the strain gauges is expressed as follows:

[0064] In the formula, ε g (p k ,t j ) indicates the strain gauge observation point p k At time t j The collected strain value, p k This represents the observation point of the k-th strain gauge; The raw strain data acquired by distributed fiber optic sensors and strain gauges constitute the raw monitoring data set E0:

[0065] In the formula, E0 represents the original strain monitoring data set used for strain field inversion. In this data set, distributed fiber optic strain data provides strain information at multiple measurement points distributed along the fiber optic path, while strain gauge data provides local strain information at key measurement points.

[0066] It should be noted that, using the physical model sample as the object to be monitored, a tunnel model and its surrounding rock area are constructed inside the sample, and the area containing the tunnel and its surrounding rock is determined as the three-dimensional computational domain for strain field inversion. Figure 2 The seismic source in the text represents the location used to apply local disturbance or dynamic load input to the physical model specimen, its function being to induce a strain response within the surrounding rock. Distributed fiber optic sensors and strain gauges are deployed around the tunnel and in its adjacent areas to acquire strain observation data under disturbance. The location, form, and loading method of the seismic source can be adjusted according to experimental or engineering monitoring needs, and are not limited to... Figure 2 As shown in the figure.

[0067] In one example of the present invention, step S30 specifically includes the following steps: S31: The strain data in the original monitoring dataset E0 undergoes outlier removal, noise filtering, baseline correction, and unit unification to reduce the impact of noise, local anomalous jumps, and initial drift on the results. For distributed fiber optic strain data, outliers can be identified based on the strain change amplitude of adjacent observation points; for strain gauge strain data, outliers can be identified based on the historical response range of the measurement point or the rate of change at adjacent times. Unify distributed fiber optic strain data and strain gauge strain data into a common time series:

[0068] In the formula, T represents the unified time series used for strain field inversion, and t j Let j represent the j-th inversion time, and m represent the total number of inversion times; When the sampling frequencies of distributed optical fibers and strain gauges are inconsistent, interpolation, resampling, or time window averaging can be used to convert data with different sampling frequencies to a unified time series T. When there is a trigger delay or response lag between different sensors, the time deviation can be corrected according to the trigger signal, characteristic peak value, or dynamic time warping algorithm (DTW) so that the optical fiber strain data and strain gauge strain data at the same inversion time have a corresponding relationship. S32: After preprocessing and time unification, at any time t j The following is a standardized strain observation data set:

[0069] Among them, E m (t j ) represents time t j The standardized strain observation data set that participates in strain field inversion, ε f (s i ,t j ) represents the observation point s along the distributed optical fiber. i The strain observation value at ε g (p k ,t j ) indicates the strain gauge observation point p k Strain observations at the location.

[0070] In one example of the present invention, such as Figure 3 As shown, step S40 specifically includes the following steps: S41: For distributed fiber strain data, the original observation points are usually represented by the distance along the distributed fiber. Therefore, a mapping relationship between the observation points along the distributed fiber and the three-dimensional spatial coordinates is established, assuming the fiber path function is:

[0071] In the formula, s represents the observation point along the distributed optical fiber, r(s) represents the spatial position function of the optical fiber path in the three-dimensional computational domain, and x represents the three-dimensional spatial coordinates corresponding to the observation point along the distributed optical fiber. For the i-th observation point s along the distributed optical fiber... i Its corresponding three-dimensional spatial coordinates are represented as:

[0072] In the formula, This represents the spatial location of the observation point along the distributed optical fiber in the three-dimensional global coordinate system O-XYZ; thus, the distributed optical fiber strain data ε f (s i ,t j This can be converted into strain observation values ​​ε at a three-dimensional spatial location. f (x i ,t j ); S42: For strain gauge strain data, determine the three-dimensional spatial coordinates of the k-th strain gauge observation point based on the actual placement of the strain gauges in the surrounding rock of the tunnel or the physical model sample:

[0073] In the formula, x k Indicates the strain gauge observation point p k Spatial position in the three-dimensional global coordinate system; thus, strain gauge strain data ε g (p k ,t j This can be represented as spatial location x. k Strain observation ε at the location g (x k ,t j ); S43: Organize the observation points along the distributed optical fiber and strain gauge observation points into a unified observation point set:

[0074] In the formula, P represents the set of observation points participating in the strain field inversion, and x h Let M represent the spatial coordinates of the h-th observation point, and M represent the total number of observation points; the observation points include distributed fiber optic observation points and strain gauge observation points. Let M be the number of distributed fiber optic observation points. f The number of strain gauge observation points is M g Then the total number of observation points satisfies M=M f +M g .

[0075] S44: At any inversion time t j Next, based on the set of observation points P and their corresponding strain observation values, the measured strain vector is constructed:

[0076] In the formula, ε m (t j ) represents time t j The measured strain vector ε participating in the inversion h (t j) indicates that the h-th observation point is at time t j Strain observations; Therefore, the multi-point strain data and strain gauge point strain data acquired by the distributed optical fiber sensor along the optical fiber path are uniformly organized into a measured strain vector under the same time reference and the same three-dimensional computational domain.

[0077] In one example of the present invention, step S50 specifically includes the following steps: S51: For any spatial location x and time t, the strain values ​​of the internal strain field of the surrounding rock at that spatial location and time can be expressed as a linear combination of several strain mode shapes and modal coordinates:

[0078] In the formula, ε(x,t) represents the strain value at spatial location x at time t; q represents the value of the r-th strain mode at position x; r (t) represents the modal coordinates of the r-th strain mode at time t; N represents the order of the strain modes involved in the reconstruction; The above expression can also be written in matrix form:

[0079] in, , ,..., Let represent the strain mode shape vector at spatial location x; q(t) = [q1(t), q2(t), ..., q N (t)] T , represents the modal coordinate vector at time t.

[0080] In one embodiment, the strain mode shapes can be obtained through one or more of the following methods: numerical simulation calculation, structural mechanics model analysis, physical model test calibration, or identification based on historical monitoring data. For example, a numerical model can be established based on the geometry of the surrounding rock of the tunnel, material parameters, and typical loading conditions to extract the strain distribution under different deformation modes as strain modes; alternatively, based on existing monitoring data, the main strain distribution features can be extracted through principal component analysis, orthogonal decomposition of features, or other modal identification methods.

[0081] S52: Store the obtained strain mode shapes according to the same three-dimensional computational domain and mesh node order to form a strain mode shape library:

[0082] In the formula, Φ represents the strain mode shape library. This represents the set of values ​​for the r-th strain mode at each grid node within the computational domain.

[0083] The modal order N can be determined based on the number of monitoring points, the size of the computational domain, the modal contribution rate, or the cross-validation results. Lower-order modes are used to characterize the overall deformation trend of the surrounding rock, while higher-order modes are used to supplement local strain concentration or gradient change characteristics.

[0084] In one example of the present invention, step S60 specifically includes the following steps: S61: The set of observation points is represented as follows:

[0085] Based on the set of observation points, extract the mode shape values ​​corresponding to each observation point from the strain mode shape library Φ constructed in step S50; for the h-th observation point x h The corresponding modal values ​​are expressed as follows:

[0086] In the formula, x h Represents the spatial coordinates of the h-th observation point. This represents the value of the r-th strain mode at the observation point, and N represents the order of the modes involved in the reconstruction. S62: Arrange the modal values ​​at all observation points in the order of observation points to construct the observation modal matrix:

[0087] In the formula, K represents the observation mode matrix, the rows of the matrix correspond to the observation points along the distributed optical fiber or the observation points of the strain gauge, and the columns of the matrix correspond to different strain modes. S63: At any inversion time t j Next, based on the measured strain vector ε constructed in step S40... m (t j Based on the observed modal matrix K, establish the transfer equation between the measured strain vector and the modal coordinates:

[0088] In the formula, ε m (t j ) represents time t j The measured strain vector below is composed of observation points along the distributed optical fiber and strain gauge observation points; q(t) j ) represents the modal coordinate vector to be solved; η(t) j ) indicates measurement noise or model error.

[0089] Therefore, the problem of reconstructing the internal strain field of the surrounding rock based on finite strain observation data is transformed into the problem of solving modal coordinates. Since the number of observation points is limited and the observation modal matrix K may have ill-conditioned properties, directly solving the modal coordinates is prone to noise amplification or unstable results. Therefore, step S70 is further executed to perform regularization solution.

[0090] In one example of the present invention, such as Figure 4 As shown, step S70 specifically includes the following steps: S71: After establishing the transfer relationship between the measured strain vector and the modal coordinates, the deviation between the measured strain vector and the calculated strain vector is used as the data fitting term, and a regularization constraint term is introduced to construct the objective function for solving the modal coordinates:

[0091] In the formula, J(q) represents the objective function to be optimized; K represents the observed mode matrix; q(t) represents the objective function to be optimized; K represents the observed mode matrix; and q(t) represents the objective function to be optimized. j ) represents time t j The modal coordinate vector to be solved; ε m (t j ) represents time t j The measured strain vector is given by λ, where λ represents the regularization parameter and R(q) represents the regularization constraint term. The regularization constraint term is used to reduce the impact of ill-conditioned observation mode matrix and monitoring noise on the inversion results, ensuring that the inversion results maintain a certain degree of spatial smoothness and stability while meeting the requirements for fitting the observation data. Preferably, the regularization constraint term includes one or more of the following: modal coordinate magnitude constraint, spatial smoothness constraint, strain gradient constraint, or weighted constraint for local high-strain regions. For example, it can take the following form:

[0092] In the formula, L represents the regularization operator, which can be set according to the modal order, spatial smoothing requirements, or strain gradient constraints. By introducing this constraint, abnormal amplification caused by higher-order modes or noise can be suppressed to a certain extent, reducing unreasonable oscillations in the inverted strain field.

[0093] Furthermore, the regularization parameter λ is used to balance the fit of the measured data with the smoothness and stability of the inversion results. When λ is small, the inversion results focus more on fitting the measured strain data; when λ is large, the inversion results focus more on satisfying the regularization constraints. In practice, λ can be determined based on the sensor noise level, the number of observation points, the modal order, or the cross-validation error.

[0094] S72: Optimize the above objective function to obtain time t. j The optimal modal coordinate vector is as follows:

[0095] In the formula, Represents time t j The modal coordinate vector that minimizes the objective function is given; the optimization solution can be completed using iterative least squares method, conjugate gradient method, Levenberg-Marquardt method or other numerical optimization algorithms.

[0096] S73: After obtaining the optimal mode coordinates corresponding to each inversion time, use the optimal mode coordinates obtained in step S70. Substituting into the strain modal expression established in step S50, we obtain time t. j Inversion strain value at any spatial location x inside the surrounding rock:

[0097] In the formula, Indicates spatial position x at time t j The inversion strain value; This represents the value of the r-th strain mode at position x; This indicates that the r-th mode occurs at time t. j The optimal modal coordinates are given; N represents the modal order involved in the reconstruction. S74: For each grid node in the three-dimensional computational domain, calculate its corresponding inversion strain value, and form the time t based on the inversion strain value on the grid node. j Reconstruction results of the strain field inside the surrounding rock:

[0098] In the formula, This represents the inversion result of the continuous strain field within the three-dimensional computational domain; where, if it is necessary to analyze the dynamic evolution process of the surrounding rock strain field, then a unified time series T={t1, t2, ..., t...} is used. m Repeat the continuous strain field inversion calculation at each inversion time point in the formula to obtain the continuous strain field sequence inside the surrounding rock: .

[0099] S75: Calculate the strain gradient, local maximum strain value and its spatial location based on the continuous strain field obtained from the inversion, and identify strain concentration zones or strain localization zones within the surrounding rock. The inversion results can be output in the form of two-dimensional profile cloud maps, three-dimensional strain cloud maps, strain gradient cloud maps or time series dynamic maps.

[0100] In one example of the present invention, after step S75, the method further includes: selecting observation points or strain gauge observation points along the distributed optical fiber that did not participate in the modal coordinate solution as verification points, calculating the difference between the inverted strain value and the measured strain value at the verification point, in order to evaluate the strain field inversion error, wherein the error expression is:

[0101] In the formula, e h (t j ) indicates that the h-th verification point is at time t. j Inversion error; This represents the inversion strain value at the verification point; ε h obs (t j ) represents the measured strain value at the verification point.

[0102] According to a second aspect of the present invention, a system for inverting the internal strain field of surrounding rock based on strain mode reconstruction includes: The unified coordinate module is configured to determine the three-dimensional computational domain for strain field inversion based on the geometry, monitoring range, and sensor deployment area of ​​the surrounding rock or physical model sample of the roadway to be monitored. It establishes a unified three-dimensional global coordinate system O-XYZ and spatially discretizes the three-dimensional computational domain to form a set of grid nodes N. m ; The data set module is configured to collect distributed fiber strain data from multiple measuring points obtained by distributed fiber optic sensors along the fiber optic deployment path, as well as point strain data obtained by strain gauges at key measuring points, and to form an original strain monitoring data set from the distributed fiber optic strain data and the strain gauge strain data. The data preprocessing module is configured to preprocess the distributed fiber optic strain data and strain gauge strain data after obtaining the original strain monitoring data set, so as to obtain standardized strain observation data under the same time series. The correspondence establishment module is configured to establish the spatial topology mapping relationship between distributed optical fibers and strain gauges, and to construct the measured strain vector: After obtaining standardized strain observation data under a unified time reference, the observation points along the distributed optical fiber and the observation points of the strain gauges are uniformly mapped to the established three-dimensional computing domain to establish the correspondence between strain observation data and spatial location, and to obtain the set of observation points and the measured strain vector. The modal mode library module is configured to build a strain mode library for reconstructing continuous strain fields within surrounding rock: after obtaining the set of observation points and measured strain vectors, it is based on a three-dimensional computational domain and a set of mesh nodes N. mWe construct all strain mode shapes used to characterize the spatial distribution of strain field inside the surrounding rock and form a strain mode shape library. By representing the continuous strain field as a combination of finite-order strain modes, we can reduce the number of unknowns caused by directly inverting the strain values ​​of all grid nodes and improve the stability of subsequent solutions.

[0103] The modal shape value module is configured to extract the modal shape values ​​at each observation point from the strain modal shape library after obtaining the strain modal shape library, construct the observation modal matrix, and establish the transfer relationship between the measured strain vector and the modal coordinates. The inversion result output module is configured to construct a regularized inversion objective function, solve for the optimal modal coordinates corresponding to each inversion time, reconstruct the internal strain field of the surrounding rock based on the strain mode mode library and the optimal modal coordinates, and output the inversion results.

[0104] This system uses multi-point strain data acquired along the fiber optic path from distributed optical fibers, along with point-based strain data from strain gauges, as inputs for inversion. The distributed optical fiber data reflects strain variation characteristics near the fiber optic path, while the strain gauge data provides local strain observation results at key locations. The combination of these two data sources provides a relatively complete observational data foundation for inverting the strain field within the surrounding rock, even with a limited number of sensors deployed.

[0105] This system establishes a spatial topological mapping relationship between distributed fiber optic coordinates, strain gauge observation points, and a three-dimensional computational domain. This transforms strain data collected by different types of sensors into a unified spatial coordinate system, forming a set of observation points and a measured strain vector. This processing method reduces the inconsistency in spatial representation of data from different sensors, enabling distributed strain data and point-based strain data to participate together in subsequent inversion calculations.

[0106] This system, based on the concept of strain mode reconstruction, represents the continuous strain field inside the surrounding rock as a combination of finite-order strain mode shapes and modal coordinates. It then extracts the modal values ​​at the observation locations from a strain mode shape library based on the set of observation points, constructing an observation mode matrix. Compared to directly inverting the strain values ​​of all spatial grid nodes, this method reduces the number of unknowns and lowers the difficulty of solving the inversion problem under limited observation data.

[0107] Based on the transfer relationship between the measured strain vector and modal coordinates, this system introduces regularization constraints to construct an inversion objective function and solves for the modal coordinates. This method can reduce the impact of ill-conditioned observation modal matrix, monitoring noise, and local outliers on the inversion results to a certain extent, ensuring that the reconstructed strain field maintains good spatial continuity and stability while meeting the requirements for fitting observation data. Based on the continuous strain field obtained by inversion, strain contour maps, strain gradient fields, and strain localization zones can be further obtained, providing a reference for surrounding rock damage evolution analysis and local deformation identification.

[0108] It should be noted that the strain field inversion system for surrounding rock based on strain mode reconstruction of the present invention can also perform any of the processing described in the strain field inversion method for surrounding rock based on strain mode reconstruction, and the specific details are not repeated here.

[0109] The foregoing description, with reference to preferred embodiments, details an exemplary implementation of the present invention’s proposed method and system for inverting the internal strain field of surrounding rock based on strain mode reconstruction. However, those skilled in the art will understand that various modifications and alterations can be made to the above specific embodiments without departing from the concept of the present invention, and various combinations can be made to the various technical features and structures proposed in the present invention without exceeding the protection scope of the present invention.

Claims

1. A method for inverting the strain field inside surrounding rock based on strain mode reconstruction, characterized in that, Includes the following steps: S10: Based on the geometry of the surrounding rock of the roadway to be monitored or the physical model sample, the monitoring range, and the sensor deployment area, determine the three-dimensional computational domain for strain field inversion, establish a unified three-dimensional global coordinate system O-XYZ, and spatially discretize the three-dimensional computational domain to form a set of grid nodes N. m ; S20: Collect distributed fiber optic strain data from multiple measuring points along the fiber optic deployment path using distributed fiber optic sensors, as well as point strain data from strain gauges at key measuring points, and form a raw strain monitoring data set from the distributed fiber optic strain data and strain gauge strain data. S30: Preprocess the distributed fiber strain data and strain gauge strain data to obtain standardized strain observation data under the same time series; S40: Map the observation points along the distributed optical fiber and the strain gauge observation points to the established three-dimensional computational domain in order to establish the correspondence between strain observation data and spatial location, and obtain the set of observation points and the measured strain vector. S50: Based on a three-dimensional computational domain and mesh node set N m Construct all strain mode shapes used to characterize the spatial distribution of strain field inside the surrounding rock, and form a strain mode shape library; S60: Based on the set of observation points, extract the mode shape values ​​at each observation point location from the strain mode shape library, construct the observation mode matrix, and establish the transfer relationship between the measured strain vector and the modal coordinates; S70: Construct a regularized inversion objective function, solve for the optimal modal coordinates corresponding to each inversion time, reconstruct the internal strain field of the surrounding rock based on the strain mode shape library and the optimal modal coordinates, and output the inversion results.

2. The method for inverting the internal strain field of surrounding rock based on strain mode reconstruction according to claim 1, characterized in that, Step S10 specifically includes the following steps: S11: Assume the region to be inverted within the surrounding rock is a three-dimensional computational domain: In the formula, Ω represents the spatial region within the surrounding rock to be inverted. Represents three-dimensional space; S12: Within the three-dimensional computational domain, any spatial location is represented as: In the formula, Let x, y, and z be the spatial position vectors, where x, y, and z are the coordinates of a point in space in the X, Y, and Z directions, respectively, and T represents the transpose. S13: For any time t, the strain field inside the surrounding rock to be inverted is composed of the strain values ​​at various spatial locations within the three-dimensional computational domain, and is expressed as: In the formula, ε(x,t) represents the value of the strain field inside the surrounding rock at spatial location x and time t; S14: Spatial discretization of the three-dimensional computational domain is performed to form multiple mesh nodes or spatial units; if node discretization is used, a set of mesh nodes is obtained: In the formula, N m x represents the set of grid nodes within the computational domain. a Let represent the spatial coordinates of the a-th grid node, and n represent the total number of grid nodes.

3. The method for inverting the internal strain field of surrounding rock based on strain mode reconstruction according to claim 1, characterized in that, Step S20 specifically includes the following steps: Distributed fiber optic sensors are deployed in the surrounding rock of the roadway to be monitored or in physical model samples. These sensors are deployed along the roadway perimeter, radially, circumferentially, along the roof and floor directions, or other predetermined paths to acquire strain data from multiple observation points distributed along the fiber optic deployment path. The distributed fiber optic strain data acquired by the distributed fiber optic sensors is expressed as follows: In the formula, ε f (s i ,t j ) represents the observation point s along the distributed optical fiber. i At time t j The collected strain values, s i Let t represent the i-th observation point along the distributed optical fiber. j Indicates the j-th sampling time; Simultaneously, strain gauges are installed on the roof, floor, sidewalls, shoulder corners, or other locations sensitive to local deformation in the roadway to obtain strain data at key locations; the strain data obtained from the strain gauges is expressed as follows: In the formula, ε g (p k ,t j ) represents the strain gauge observation point p k At time t j The collected strain value, p k This represents the observation point of the k-th strain gauge; The raw strain data acquired by distributed fiber optic sensors and strain gauges constitute the raw monitoring data set E0: In the formula, E0 represents the set of original strain monitoring data used for strain field inversion.

4. The method for inverting the internal strain field of surrounding rock based on strain mode reconstruction according to claim 1, characterized in that, Step S30 specifically includes the following steps: S31: Perform outlier removal, noise filtering, baseline correction, and unit unification on the strain data in the original monitoring data set E0. For distributed fiber optic strain data, outliers are identified based on the strain change amplitude of adjacent observation points. For strain gauge strain data, outliers are identified based on the historical response range of the measurement point or the rate of change at adjacent times. Unify distributed fiber optic strain data and strain gauge strain data into a common time series: In the formula, T represents the unified time series used for strain field inversion, and t j Let j represent the j-th inversion time, and m represent the total number of inversion times; S32: After preprocessing and time unification, at any time t j The following is a standardized strain observation data set: Among them, E m (t j ) represents time t j The standardized strain observation data set that participates in strain field inversion, ε f (s i ,t j ) represents the observation point s along the distributed optical fiber. i The strain observation value at ε g (p k ,t j ) represents the strain gauge observation point p k Strain observations at the location.

5. The method for inverting the internal strain field of surrounding rock based on strain mode reconstruction according to claim 1, characterized in that, Step S40 specifically includes the following steps: S41: For distributed fiber strain data, the original observation points are represented by the distance along the distributed fiber. Therefore, a mapping relationship between the observation points along the distributed fiber and the three-dimensional spatial coordinates is established, assuming the fiber path function is: In the formula, s represents the observation point along the distributed optical fiber, r(s) represents the spatial position function of the optical fiber path in the three-dimensional computational domain, and x represents the three-dimensional spatial coordinates corresponding to the observation point along the distributed optical fiber. For the i-th observation point s along the distributed optical fiber... i Its corresponding three-dimensional spatial coordinates are represented as: In the formula, This represents the spatial location of the observation point along the distributed optical fiber in the three-dimensional global coordinate system O-XYZ; thus, the distributed optical fiber strain data ε f (s i ,t j Converted to strain observation values ​​ε at a three-dimensional spatial location f (x i ,t j ); S42: For strain gauge strain data, determine the three-dimensional spatial coordinates of the k-th strain gauge observation point based on the actual placement of the strain gauges in the surrounding rock of the tunnel or the physical model sample: In the formula, x k Indicates the strain gauge observation point p k Spatial position in the three-dimensional global coordinate system; thus, strain gauge strain data ε g (p k ,t j ) represents the spatial location x k Strain observation ε at the location g (x k ,t j ); S43: Organize the observation points along the distributed optical fiber and strain gauge observation points into a unified observation point set: In the formula, P represents the set of observation points participating in the strain field inversion, and x h Let H represent the spatial coordinates of the h-th observation point, and M represent the total number of observation points. S44: At any inversion time t j Next, based on the set of observation points P and their corresponding strain observation values, the measured strain vector is constructed: In the formula, ε m (t j ) represents time t j The measured strain vector ε participating in the inversion h (t j ) indicates that the h-th observation point is at time t j The strain observation values.

6. The method for inverting the internal strain field of surrounding rock based on strain mode reconstruction according to claim 1, characterized in that, Step S50 specifically includes the following steps: S51: For any spatial location x and time t, the strain values ​​of the internal strain field of the surrounding rock at that spatial location and time can be expressed as a linear combination of the Nth order strain mode shape and the modal coordinates: In the formula, ε(x,t) represents the strain value at spatial location x at time t; q represents the value of the r-th strain mode at position x; r (t) represents the modal coordinates of the r-th strain mode at time t; N represents the order of the strain modes involved in the reconstruction; S52: Store the obtained strain mode shapes according to the same three-dimensional computational domain and mesh node order to form a strain mode shape library: In the formula, Φ represents the strain mode shape library. This represents the set of values ​​for the r-th strain mode at each grid node within the computational domain.

7. The method for inverting the internal strain field of surrounding rock based on strain mode reconstruction according to claim 1, characterized in that, Step S60 specifically includes the following steps: S61: Based on the set of observation points, extract the mode shape values ​​corresponding to each observation point from the constructed strain mode shape library Φ; for the h-th observation point x h The corresponding modal values ​​are expressed as follows: In the formula, x h Represents the spatial coordinates of the h-th observation point. The value of the r-th strain mode at the observation point is represented by N, where N represents the order of the modes involved in the reconstruction. S62: Arrange the modal values ​​at all observation points in the order of observation points to construct the observation modal matrix: In the formula, K represents the observation mode matrix, the rows of the matrix correspond to the observation points along the distributed optical fiber or the observation points of the strain gauge, and the columns of the matrix correspond to different strain modes. S63: At any inversion time t j Below, based on the constructed measured strain vector ε m (t j Based on the observed modal matrix K, establish the transfer equation between the measured strain vector and the modal coordinates: In the formula, ε m (t j ) represents time t j The measured strain vector below is composed of observation points along the distributed optical fiber and strain gauge observation points; q(t) j ) represents the modal coordinate vector to be solved; η(t) j ) indicates measurement noise or model error.

8. The method for inverting the internal strain field of surrounding rock based on strain mode reconstruction according to claim 1, characterized in that, Step S70 specifically includes the following steps: S71: Using the deviation between the measured strain vector and the calculated strain vector as the data fitting term, and introducing a regularization constraint term, an objective function is constructed to solve for the modal coordinates: In the formula, J(q) represents the objective function to be optimized; K represents the observed mode matrix; q(t) represents the objective function to be optimized; K represents the observed mode matrix; and q(t) represents the objective function to be optimized. j ) represents time t j The modal coordinate vector to be solved; ε m (t j ) represents time t j The measured strain vector is given by λ, where λ represents the regularization parameter and R(q) represents the regularization constraint term. S72: Optimize the objective function to obtain time t. j The optimal modal coordinate vector is as follows: In the formula, Represents time t j The modal coordinate vector that minimizes the objective function; S73: Obtain the optimal modal coordinates Substituting into the established strain modal expression, we obtain time t. j Inversion strain value at any spatial location x inside the surrounding rock: In the formula, Indicates spatial position x at time t j The inversion strain value; This represents the value of the r-th strain mode at position x; This indicates that the r-th mode occurs at time t. j The optimal modal coordinates are given; N represents the modal order involved in the reconstruction. S74: For each grid node in the three-dimensional computational domain, calculate its corresponding inversion strain value, and form the time t based on the inversion strain value on the grid node. j Reconstruction results of the strain field inside the surrounding rock: In the formula, This represents the inversion result of the continuous strain field within the three-dimensional computational domain; where, if it is necessary to analyze the dynamic evolution process of the surrounding rock strain field, then a unified time series T={t1, t2, ..., t... is used. m Repeat the continuous strain field inversion calculation at each inversion time point in the formula to obtain the continuous strain field sequence inside the surrounding rock: S75: Calculate the strain gradient, local maximum strain value and its spatial location based on the continuous strain field obtained by inversion, and identify strain concentration areas or strain localization zones inside the surrounding rock.

9. The method for inverting the internal strain field of surrounding rock based on strain mode reconstruction according to claim 8, characterized in that, Following step S75, the method further includes: selecting observation points or strain gauge observation points along the distributed optical fiber that were not involved in the modal coordinate solution as verification points, calculating the difference between the inverted strain value and the measured strain value at the verification point, to evaluate the strain field inversion error. The error expression is as follows: In the formula, e h (t j ) indicates that the h-th verification point is at time t. j Inversion error; This represents the inversion strain value at the verification point; ε h obs (t j ) represents the measured strain value at the verification point.

10. A system for inverting the strain field inside surrounding rock based on strain mode reconstruction, characterized in that, include: The unified coordinate module is configured to determine the three-dimensional computational domain for strain field inversion based on the geometry, monitoring range, and sensor deployment area of ​​the surrounding rock or physical model sample of the roadway to be monitored. It establishes a unified three-dimensional global coordinate system O-XYZ and spatially discretizes the three-dimensional computational domain to form a set of grid nodes N. m ; The data set module is configured to collect distributed fiber strain data from multiple measuring points obtained by distributed fiber optic sensors along the fiber optic deployment path, as well as point strain data obtained by strain gauges at key measuring points, and to form an original strain monitoring data set from the distributed fiber optic strain data and the strain gauge strain data. The data preprocessing module is configured to preprocess distributed fiber strain data and strain gauge strain data to obtain standardized strain observation data under the same time series. The correspondence establishment module is configured to uniformly map the observation points along the distributed optical fiber and the strain gauge observation points to the established three-dimensional computing domain, so as to establish the correspondence between strain observation data and spatial location, and obtain the set of observation points and the measured strain vector. The modal shape library module is configured based on a three-dimensional computational domain and a set of mesh nodes N. m Construct all strain mode shapes used to characterize the spatial distribution of strain field inside the surrounding rock, and form a strain mode shape library; The modal shape value module is configured to extract the modal shape values ​​at each observation point from the strain modal shape library after obtaining the strain modal shape library, construct the observation modal matrix, and establish the transfer relationship between the measured strain vector and the modal coordinates. The inversion result output module is configured to construct a regularized inversion objective function, solve for the optimal modal coordinates corresponding to each inversion time, reconstruct the internal strain field of the surrounding rock based on the strain mode mode library and the optimal modal coordinates, and output the inversion results.

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