Tensor decomposition modeling method with constraint for tunnel construction monitoring

Abstract

The embodiment of the application is suitable for the technical field of tunnel monitoring, and provides a tensor decomposition modeling method with constraints for tunnel construction monitoring, which comprises the following steps: determining a tensor based on tunnel construction monitoring data, wherein the tunnel construction monitoring data comprises a plurality of sampling data, each sampling data comprises feature data of a plurality of dimensions, and each sampling data has corresponding time information and position information; determining a factor matrix of the tensor, wherein the factor matrix comprises a time factor matrix, a space factor matrix and a feature factor matrix; optimizing the factor matrix to obtain a target factor matrix satisfying time constraints, space constraints and physical constraints; and performing tensor reconstruction according to the target factor matrix to obtain an optimized target tensor. Through the above method, the tensor corresponding to the tunnel construction monitoring data can be optimized, so that the accuracy of tunnel construction monitoring is improved.

Description

Technical Field

[0001] This application belongs to the field of tunnel monitoring technology, and in particular relates to a constrained tensor decomposition modeling method for tunnel construction monitoring. Background Technology

[0002] During tunnel operation, the structural health is crucial to its safety and reliability. By deploying sensors inside the tunnel, multi-dimensional spatiotemporal monitoring data such as stress, strain, displacement, and temperature can be obtained.

[0003] However, the collected tunnel monitoring data may be incomplete. For example, due to sensor malfunctions, data transmission errors, or other reasons, the collected tunnel monitoring data may contain missing information.

[0004] Incomplete monitoring data can affect the monitoring of tunnel structures, leading to inaccurate tunnel construction monitoring. Summary of the Invention

[0005] In view of this, embodiments of this application provide a constrained tensor decomposition modeling method for tunnel construction monitoring, which optimizes the tensors corresponding to tunnel construction monitoring data, thereby improving the accuracy of tunnel construction monitoring.

[0006] The first aspect of this application provides a constrained tensor decomposition modeling method for tunnel construction monitoring, including:

[0007] Tensors are determined based on tunnel construction monitoring data, which includes multiple sample data, each sample data includes feature data in multiple dimensions, and each sample data has corresponding time information and location information.

[0008] Determine the factor matrix of the tensor, wherein the factor matrix includes a time factor matrix, a spatial factor matrix, and a feature factor matrix;

[0009] The factor matrix is ​​optimized to obtain a target factor matrix that satisfies time constraints, space constraints, and physical constraints.

[0010] Based on the target factor matrix, tensor reconstruction is performed to obtain the optimized target tensor.

[0011] A second aspect of this application provides a constrained tensor decomposition modeling device for tunnel construction monitoring, comprising:

[0012] The tensor determination module is used to determine tensors based on tunnel construction monitoring data. The tunnel construction monitoring data includes multiple sample data, each sample data includes feature data in multiple dimensions, and each sample data has corresponding time information and location information.

[0013] A matrix determination module is used to determine the factor matrix of the tensor, wherein the factor matrix includes a time factor matrix, a spatial factor matrix, and a feature factor matrix.

[0014] The matrix optimization module is used to optimize the factor matrix to obtain a target factor matrix that satisfies time constraints, space constraints, and physical constraints.

[0015] The tensor optimization module is used to reconstruct the tensor based on the target factor matrix to obtain the optimized target tensor.

[0016] A third aspect of this application provides a computer device including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the method described in the first aspect above.

[0017] A fourth aspect of this application provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the method described in the first aspect above.

[0018] A fifth aspect of this application provides a computer program product that, when run on a computer device, causes the computer device to perform the method described in the first aspect.

[0019] Compared with the prior art, the embodiments of this application have the following advantages:

[0020] The method described in this application embodiment can optimize the tensor corresponding to tunnel construction monitoring data, making the tensor more accurate and beneficial for tunnel construction monitoring. The computer device can determine the tensor of the tunnel construction monitoring data. Since the tunnel construction monitoring data includes multiple sample data points, each sample data point includes multi-dimensional feature data, and each sample data point has corresponding time and location information, the tensor corresponding to the tunnel construction monitoring data should have corresponding physical and spatiotemporal characteristics. When optimizing the tensor, the optimized tensor should satisfy physical and spatiotemporal constraints. Therefore, the computer device can decompose the tensor to obtain a time factor matrix, a spatial factor matrix, and a feature factor matrix; then, the computer device can optimize the factor matrix to obtain a target factor matrix that satisfies the time, spatial, and physical constraints. Based on the target factor matrix that satisfies the time, spatial, and physical constraints, tensor reconstruction can be performed to obtain the optimized target tensor. The original tensor is determined based on the collected tunnel construction monitoring data, which may contain errors or omissions; therefore, the obtained tensor is not accurate enough. The method in this embodiment can optimize the tensor corresponding to tunnel construction monitoring data. The optimized target tensor satisfies time constraints, spatial constraints, and physical constraints. This is equivalent to correcting errors and omissions in the original tunnel construction monitoring data within the tensor based on these constraints, thus obtaining a more accurate target tensor. Using the target tensor for tunnel construction monitoring can improve the accuracy of tunnel construction monitoring. Attached Figure Description

[0021] To more clearly illustrate the technical solutions in the embodiments of this application, the accompanying drawings used in the description of the embodiments or the prior art will be briefly introduced below.

[0022] Figure 1 This is a flowchart illustrating the steps of a constrained tensor decomposition modeling method for tunnel construction monitoring provided in an embodiment of this application.

[0023] Figure 2 This is a flowchart illustrating the steps of another constrained tensor decomposition modeling method for tunnel construction monitoring provided in this application embodiment;

[0024] Figure 3 This is a schematic diagram of a constrained tensor decomposition modeling device for tunnel construction monitoring provided in an embodiment of this application;

[0025] Figure 4 This is a schematic diagram of a computer device provided in an embodiment of this application. Detailed Implementation

[0026] In the following description, specific details such as particular system architectures and techniques are set forth for illustrative purposes and not for limitation, in order to provide a thorough understanding of the embodiments of this application. However, those skilled in the art will understand that this application may also be implemented in other embodiments without these specific details. In other instances, detailed descriptions of well-known systems, apparatuses, circuits, and methods have been omitted so as not to obscure the description of this application with unnecessary detail.

[0027] During tunnel operation, the structural health is crucial to its safety and reliability. Sensors are deployed inside the tunnel to acquire multi-dimensional spatiotemporal monitoring data, including stress, strain, displacement, and temperature. However, this data is large and complex, and traditional analysis methods struggle to fully extract its potential information and effectively predict the structure's future condition.

[0028] Tensor decomposition is an effective tool for processing multidimensional data, but traditional tensor decomposition methods fail to take into account the physical characteristics of tunnel structures and the spatiotemporal correlation of monitoring data, resulting in limited physical interpretability and predictive ability of the model.

[0029] This application provides a constrained tensor decomposition modeling method for tunnel construction monitoring, which can improve the accuracy of tunnel construction monitoring.

[0030] The technical solution of this application will be described below through specific embodiments.

[0031] Reference Figure 1 This document illustrates a flowchart of a constrained tensor decomposition modeling method for tunnel construction monitoring, provided in an embodiment of this application. The method may specifically include the following steps:

[0032] S101, determine the tensor based on tunnel construction monitoring data, wherein the tunnel construction monitoring data includes multiple sample data, each sample data includes feature data of multiple dimensions, and each sample data has corresponding time information and location information.

[0033] This embodiment can be executed by a computer device. The computer device can be a mobile phone, tablet computer, wearable device, laptop computer, ultra-mobile personal computer (UMPC), netbook, personal digital assistant (PDA), etc. This application embodiment does not limit the specific type of computer device.

[0034] In this embodiment, tunnel construction monitoring data may include feature dimensions of multiple sampled data, time information corresponding to each sampled data, and location information of each sampled data. The tunnel construction monitoring data can be acquired from a data acquisition device, which may include multiple sensors, each of which can be installed at a corresponding location for sampling. The time information of the sampled data can be the sampling time, and the location information can be the sensor location.

[0035] In this embodiment, the sampling data may include bridge structural health data, tunnel structural health data, or detection image data, etc.

[0036] S102, determine the factor matrix of the tensor, the factor matrix including the time factor matrix, the spatial factor matrix and the characteristic factor matrix.

[0037] In one possible implementation, the tensor can be decomposed to obtain a factor matrix. In this embodiment, the tensor can be input into a tensor decomposition model to obtain the feature factor matrix, time factor matrix, and spatial factor matrix of the data set to be detected.

[0038] As an example, the factor matrix of a tensor can be obtained through CP (CANDECOMP / PARAFAC) decomposition. Specifically, CP decomposition decomposes the tensor into the product of three factor matrices. For example, the factor matrix of the tensor can be determined using the following formula:

[0039]

[0040] A = [a1, a2, ..., a] r , ..., a R ]

[0041] B = [b1, b2, ..., b r , ..., b R ]

[0042] C = [c1, c2, ..., c r c R ]

[0043] in, Let R be a tensor, A be the time factor matrix, B be the space factor matrix, and C be the eigenfactor matrix. The representation performs the vector outer product operation.

[0044] S103, optimize the factor matrix to obtain the target factor matrix that satisfies the time constraint, space constraint and physical constraint.

[0045] Obtain the auxiliary time factor matrix that satisfies the spatiotemporal kriging constraint, the auxiliary space factor matrix that satisfies the spatiotemporal kriging constraint, and the auxiliary feature factor matrix that satisfies the physical constraint.

[0046] An optimization formula is constructed based on the auxiliary time factor matrix, auxiliary space factor matrix, and auxiliary feature factor matrix.

[0047] Based on the optimization formula, the optimized target time factor matrix, target space factor matrix, and target feature factor matrix are obtained.

[0048] We introduce auxiliary factor matrices A0, B0, and C0, where A0 is the time factor matrix that satisfies the spatiotemporal kriging constraint, B0 is the space factor matrix that satisfies the spatiotemporal kriging constraint, and C0 is the feature factor matrix that satisfies the physical constraint.

[0049] Specifically, Hooke's Law is introduced as a physical constraint. The formula for Hooke's Law is:

[0050] σ=E·ε

[0051] Where σ is stress, E is elastic modulus (a known constant), and ε is strain.

[0052] Specifically, the physical constraints are represented in the model, assuming that stress and strain correspond to f=1 and f=2 respectively in the feature dimensions. In the feature factor matrix C, the corresponding rows are taken: C σ =E·C ε .

[0053] Specifically, a spatiotemporal kriging model is introduced as a constraint on the time and space factor matrices to describe the correlations within them. The time dimension constraint is based on the time-dependent variogram γ. T (u) Construct the time covariance matrix K T The covariance of the time factor matrix is ​​close to K. T AA T ≈K T Spatial dimensional constraints: based on the spatial variogram γ S (h) Construct the spatial covariance matrix K S The covariance of the spatial factor matrix is ​​close to K. S BB T ≈K S .

[0054] Based on the auxiliary time factor matrix, auxiliary space factor matrix, and auxiliary feature factor matrix, an optimization formula is constructed, including:

[0055]

[0056] Where ρ1, ρ2, and ρ3 are penalty parameters. Let A be a tensor, A be the time factor matrix, B be the space factor matrix, C be the characteristic factor matrix, A0 be the auxiliary time factor matrix, B0 be the auxiliary space factor matrix, C0 be the auxiliary characteristic factor matrix, and E be a constant. and These are the rows corresponding to stress and strain in C0, respectively.

[0057] Based on the optimization formula, the optimized target time factor matrix, target space factor matrix, and target feature factor matrix are obtained, including:

[0058] The optimization formula is converted into multiple iterative formulas, which correspond to the time factor matrix, the space factor matrix, and the feature factor matrix, respectively.

[0059] Based on the iterative formula, the time factor matrix, spatial factor matrix, and characteristic factor matrix are iterated separately;

[0060] Determine whether the time factor matrix, space factor matrix, and eigenfactor matrix after iteration satisfy the convergence condition;

[0061] If the convergence condition is met, the iterated time factor matrix, spatial factor matrix, and eigenfactor matrix will be used as the target time factor matrix, target spatial factor matrix, and target eigenfactor matrix, respectively.

[0062] If the convergence condition is not met, the target step and the steps following the target step are executed until the convergence condition is met. The target step is based on an iterative formula, which iterates the time factor matrix, the spatial factor matrix, and the eigenfactor matrix respectively.

[0063] Iterative formulas include:

[0064]

[0065]

[0066] Among them, A k+1 Let B be the time factor matrix after the (k+1)th iteration. k+1 Let C be the spatial factor matrix after the (k+1)th iteration. k+1 This is the eigenfactor matrix after the (k+1)th iteration. This is the auxiliary time factor matrix after the (k+1)th iteration. This is the auxiliary space factor matrix after the (k+1)th iteration. This is the auxiliary feature factor matrix after the (k+1)th iteration. and Let A be the Lagrange multiplier after the (k+1)th iteration. k Let B be the time factor matrix after the k-th iteration.k Let C be the spatial factor matrix after the k-th iteration. k The eigenfactor matrix after the k-th iteration is... This is the auxiliary time factor matrix after the k-th iteration. Let be the auxiliary space factor matrix after the k-th iteration. This is the auxiliary feature factor matrix after the k-th iteration. and Let ρ1, ρ2, ρ3 be the Lagrange multipliers after the k-th iteration, and let ρ1, ρ2, ρ3 be the penalty parameters. Let E be a tensor and E be a constant. and These are the rows corresponding to stress and strain in C0, respectively.

[0067] The convergence condition is:

[0068]

[0069] Among them, A k+1 Let B be the time factor matrix after the (k+1)th iteration. k+1 Let C be the spatial factor matrix after the (k+1)th iteration. k+1 This is the eigenfactor matrix after the (k+1)th iteration. This is the auxiliary time factor matrix after the (k+1)th iteration. This is the auxiliary space factor matrix after the (k+1)th iteration. Let be the auxiliary feature factor matrix after the (k+1)th iteration, where ∈1, ∈2 and ∈3 are constants.

[0070] S104. Based on the target factor matrix, perform tensor reconstruction to obtain the optimized target tensor.

[0071] In this embodiment, the tensor can be optimized so that the tunnel construction monitoring data can be corrected in the optimized tensor, thereby obtaining more accurate monitoring results based on the optimized tensor.

[0072] This application proposes a constrained tensor decomposition modeling method that incorporates the physical formulas of the tunnel structure and the spatiotemporal Kriging model as constraints into the tensor decomposition process. This method improves the physical interpretability of the model, enhances its predictive ability for unobserved data, and provides a scientific basis for the safety assessment and maintenance of tunnel structures.

[0073] Reference Figure 2 This illustration shows a flowchart of another constrained tensor decomposition modeling method for tunnel construction monitoring provided in this application embodiment, which may specifically include the following steps:

[0074] S201, Determine the tensor based on tunnel construction monitoring data, wherein the tunnel construction monitoring data includes multiple sample data, each sample data includes feature data of multiple dimensions, and each sample data has corresponding time information and location information.

[0075] S202, determine the factor matrix of the tensor, the factor matrix including the time factor matrix, the spatial factor matrix and the feature factor matrix.

[0076] S203, optimize the factor matrix to obtain a target factor matrix that satisfies time constraints, space constraints and physical constraints.

[0077] S204. Based on the target factor matrix, perform tensor reconstruction to obtain the optimized target tensor.

[0078] S205, Analyze the tunnel structure based on the target tensor.

[0079] Specifically, the reconstruction error is the error between the decomposed tensor and the original tensor, used to evaluate the model's fit.

[0080] Specifically, physical constraint satisfaction is a check The value should be close to zero;

[0081] Specifically, spatiotemporal correlation is calculated and K T The difference was used to verify whether the covariance of the time factor matrix met expectations.

[0082] Specifically, visualization involves plotting the factor matrix to observe whether there are obvious structural features. Prediction uses the decomposition results to predict the structural response at unobserved locations or future time points, and compares it with the actual observed data.

[0083] This application first obtains the time factor matrix, spatial factor matrix, and feature factor matrix of the monitoring data set. Based on physical constraints and spatiotemporal kriging constraints, it obtains a constrained tensor of the monitoring data set. Compared with the prior art, which only uses the time factor matrix, spatial factor matrix, and feature factor matrix to obtain the tensor result of the data, this application uses physical constraints and spatiotemporal kriging constraints to analyze the data, and obtains a more accurate tensor result of the data.

[0084] It should be noted that the sequence number of each step in the above embodiments does not imply the order of execution. The execution order of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiments of this application.

[0085] Reference Figure 3The diagram illustrates a constrained tensor decomposition modeling device for tunnel construction monitoring provided in this application embodiment. Specifically, the device may include a tensor determination module 31, a matrix determination module 32, a matrix optimization module 33, and a tensor optimization module 34, wherein:

[0086] Tensor determination module 31 is used to determine tensors based on tunnel construction monitoring data. The tunnel construction monitoring data includes multiple sample data, each sample data includes feature data in multiple dimensions, and each sample data has corresponding time information and location information.

[0087] The matrix determination module 32 is used to determine the factor matrix of the tensor, the factor matrix including a time factor matrix, a spatial factor matrix and a feature factor matrix;

[0088] The matrix optimization module 33 is used to optimize the factor matrix to obtain a target factor matrix that satisfies time constraints, space constraints and physical constraints;

[0089] Tensor optimization module 34 is used to reconstruct the tensor based on the target factor matrix to obtain the optimized target tensor.

[0090] In one possible implementation, the factor matrix of the tensor is determined by the following formula:

[0091]

[0092] A = [a1, a2, ..., a] r , ..., a R ]

[0093] B = [b1, b2, ..., b r , ..., b R ]

[0094] C = [c1, c2, ..., c r c R ]

[0095] in, Let R be the tensor, A be the time factor matrix, B be the spatial factor matrix, and C be the eigenfactor matrix. The representation performs the vector outer product operation.

[0096] In one possible implementation, optimizing the factor matrix to obtain a target factor matrix that satisfies time constraints, space constraints, and physical constraints includes:

[0097] Obtain the auxiliary time factor matrix that satisfies the spatiotemporal kriging constraint, the auxiliary space factor matrix that satisfies the spatiotemporal kriging constraint, and the auxiliary feature factor matrix that satisfies the physical constraint.

[0098] Based on the auxiliary time factor matrix, the auxiliary space factor matrix, and the auxiliary feature factor matrix, an optimization formula is constructed.

[0099] Based on the optimization formula, the optimized target time factor matrix, target space factor matrix, and target feature factor matrix are obtained.

[0100] In one possible implementation, constructing the optimization formula based on the auxiliary time factor matrix, the auxiliary space factor matrix, and the auxiliary feature factor matrix includes:

[0101]

[0102] Where ρ1, ρ2, and ρ3 are penalty parameters. Let A be the tensor, B be the time factor matrix, C be the spatial factor matrix, A0 be the auxiliary time factor matrix, B0 be the auxiliary spatial factor matrix, C0 be the auxiliary feature factor matrix, and E be a constant. and These are the rows corresponding to stress and strain in C0, respectively.

[0103] In one possible implementation, obtaining the optimized target time factor matrix, target space factor matrix, and target feature factor matrix according to the optimization formula includes:

[0104] The optimization formula is converted into multiple iterative formulas, and the iterative formulas correspond to the time factor matrix, the space factor matrix, and the feature factor matrix, respectively.

[0105] Based on the iterative formula, the time factor matrix, the spatial factor matrix, and the feature factor matrix are iterated respectively.

[0106] Determine whether the time factor matrix, the space factor matrix, and the feature factor matrix after iteration satisfy the convergence condition;

[0107] If the convergence condition is met, the iterated time factor matrix, the spatial factor matrix, and the feature factor matrix are respectively used as the target time factor matrix, the target spatial factor matrix, and the target feature factor matrix.

[0108] If the convergence condition is not met, the target step and the steps following the target step are executed until the convergence condition is met. The target step is to iterate the time factor matrix, the spatial factor matrix, and the feature factor matrix based on the iterative formula.

[0109] In one possible implementation, the iterative formula includes:

[0110]

[0111] Among them, A k+1 B is the time factor matrix after the (k+1)th iteration. k+1 Let C be the spatial factor matrix after the (k+1)th iteration. k+1 The feature factor matrix after the (k+1)th iteration is given. This is the auxiliary time factor matrix after the (k+1)th iteration. Let be the auxiliary space factor matrix after the (k+1)th iteration. The auxiliary feature factor matrix after the (k+1)th iteration is given. and Let A be the Lagrange multiplier after the (k+1)th iteration. k Let B be the time factor matrix after the k-th iteration. k Let C be the spatial factor matrix after the k-th iteration. k Let be the feature factor matrix after the k-th iteration. Let be the auxiliary time factor matrix after the k-th iteration. Let be the auxiliary space factor matrix after the k-th iteration. Let be the auxiliary feature factor matrix after the k-th iteration. and Let ρ1, ρ2, ρ3 be the Lagrange multipliers after the k-th iteration, and let ρ1, ρ2, ρ3 be the penalty parameters. Let E be the tensor, and E be a constant. and These are the rows corresponding to stress and strain in C0, respectively.

[0112] In one possible implementation, the convergence condition is:

[0113]

[0114] Among them, A k+1 B is the time factor matrix after the (k+1)th iteration. k+1 Let C be the spatial factor matrix after the (k+1)th iteration. k+1 The feature factor matrix after the (k+1)th iteration is given. This is the auxiliary time factor matrix after the (k+1)th iteration. Let be the auxiliary space factor matrix after the (k+1)th iteration. Let be the auxiliary feature factor matrix after the (k+1)th iteration, where ∈1, ∈2 and ∈3 are constants.

[0115] In one possible implementation, after tensor reconstruction based on the target factor matrix to obtain the optimized target tensor, the following steps are included:

[0116] Analyze the tunnel structure based on the target tensor.

[0117] As the apparatus embodiments are basically similar to the method embodiments, they are described in a relatively simple manner. For relevant details, please refer to the description in the method embodiment section.

[0118] Figure 4 This is a schematic diagram of the structure of a computer device provided in an embodiment of this application. Figure 4 As shown, the computer device 4 of this embodiment includes: at least one processor 40 ( Figure 4 (Only one is shown in the diagram), memory 41, and computer program 42 stored in said memory 41 and executable on said at least one processor 40, which, when executed, implements the steps in any of the above method embodiments.

[0119] The computer device 4 can be a desktop computer, laptop, handheld computer, or cloud computing device, etc. This computer device may include, but is not limited to, a processor 40 and a memory 41. Those skilled in the art will understand that... Figure 4 The computer device 4 is merely an example and does not constitute a limitation on the computer device 4. It may include more or fewer components than shown, or combine certain components, or different components, such as input / output devices, network access devices, etc.

[0120] The processor 40 may be a Central Processing Unit (CPU), or it may be other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. A general-purpose processor may be a microprocessor or any conventional processor.

[0121] In some embodiments, the memory 41 may be an internal storage unit of the computer device 4, such as a hard disk or memory of the computer device 4. In other embodiments, the memory 41 may be an external storage device of the computer device 4, such as a plug-in hard disk, smart media card (SMC), secure digital card (SD), flash card, etc., equipped on the computer device 4. Furthermore, the memory 41 may include both internal and external storage units of the computer device 4. The memory 41 is used to store the operating system, applications, bootloader, data, and other programs, such as the program code of the computer program. The memory 41 can also be used to temporarily store data that has been output or will be output.

[0122] This application also provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the steps described in the various method embodiments above.

[0123] This application provides a computer program product that, when run on a computer device, enables the computer device to perform the steps described in the above-described method embodiments.

[0124] The embodiments described above are only used to illustrate the technical solutions of this application, and are not intended to limit it. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this application, and should all be included within the protection scope of this application.

Claims

1. A constrained tensor decomposition modeling method for tunnel construction monitoring, characterized in that, include: Tensors are determined based on tunnel construction monitoring data, which includes multiple sample data, each sample data includes feature data in multiple dimensions, and each sample data has corresponding time information and location information. The factor matrix of the tensor is determined by CP decomposition. The factor matrix includes a time factor matrix, a spatial factor matrix, and an eigenvalue factor matrix. The tensor is decomposed into a product of factor matrices. The factor matrix is ​​optimized to obtain a target factor matrix that satisfies time constraints, space constraints, and physical constraints, wherein the physical constraint is Hooke's law. Based on the target factor matrix, tensor reconstruction is performed to obtain the optimized target tensor; Analyze the tunnel structure based on the target tensor; The optimization of the factor matrix to obtain a target factor matrix that satisfies time constraints, space constraints, and physical constraints includes: Obtain the auxiliary time factor matrix that satisfies the spatiotemporal kriging constraint, the auxiliary space factor matrix that satisfies the spatiotemporal kriging constraint, and the auxiliary feature factor matrix that satisfies the physical constraint. Based on the auxiliary time factor matrix, the auxiliary space factor matrix, and the auxiliary feature factor matrix, an optimization formula is constructed. Based on the optimization formula, the optimized target time factor matrix, target space factor matrix, and target feature factor matrix are obtained.

2. The method as described in claim 1, characterized in that, The factor matrix of the tensor is determined by the following formula: in, For the tensor, Let be the rank used for tensor decomposition. The time factor matrix, For the space factor matrix, The feature factor matrix, The representation performs the vector outer product operation.

3. The method as described in claim 2, characterized in that, The optimization formula is constructed based on the auxiliary time factor matrix, the auxiliary space factor matrix, and the auxiliary feature factor matrix, including: in, For penalty parameters, Let A be the tensor, B be the time factor matrix, and C be the spatial factor matrix. The auxiliary time factor matrix, The auxiliary space factor matrix, The auxiliary feature factor matrix, It is a constant. and They are respectively The corresponding rows for stress and strain.

4. The method as described in claim 3, characterized in that, The step of obtaining the optimized target time factor matrix, target space factor matrix, and target feature factor matrix according to the optimization formula includes: The optimization formula is converted into multiple iterative formulas, and the iterative formulas correspond to the time factor matrix, the space factor matrix, and the feature factor matrix, respectively. Based on the iterative formula, the time factor matrix, the spatial factor matrix, and the feature factor matrix are iterated respectively. Determine whether the time factor matrix, the space factor matrix, and the feature factor matrix after iteration satisfy the convergence condition; If the convergence condition is met, the iterated time factor matrix, the spatial factor matrix, and the feature factor matrix are respectively used as the target time factor matrix, the target spatial factor matrix, and the target feature factor matrix. If the convergence condition is not met, the target step and the steps following the target step are executed until the convergence condition is met. The target step is to iterate the time factor matrix, the spatial factor matrix, and the feature factor matrix based on the iterative formula.

5. The method as described in claim 4, characterized in that, The iterative formula includes: in, The time factor matrix after the (k+1)th iteration is given. Let be the spatial factor matrix after the (k+1)th iteration. The feature factor matrix after the (k+1)th iteration is given. This is the auxiliary time factor matrix after the (k+1)th iteration. Let be the auxiliary space factor matrix after the (k+1)th iteration. The auxiliary feature factor matrix after the (k+1)th iteration is given. , and For the (k+1)th iteration, the Lagrange multiplier is... Let be the time factor matrix after the k-th iteration. Let be the space factor matrix after the k-th iteration. Let be the feature factor matrix after the k-th iteration. Let be the auxiliary time factor matrix after the k-th iteration. Let be the auxiliary space factor matrix after the k-th iteration. Let be the auxiliary feature factor matrix after the k-th iteration. , and For the Lagrange multipliers after the k-th iteration, For penalty parameters, For the tensor, It is a constant. and They are respectively The corresponding rows for stress and strain.

6. The method as described in claim 4, characterized in that, The convergence condition is: in, The time factor matrix after the (k+1)th iteration is given. Let be the spatial factor matrix after the (k+1)th iteration. The feature factor matrix after the (k+1)th iteration is given. This is the auxiliary time factor matrix after the (k+1)th iteration. Let be the auxiliary space factor matrix after the (k+1)th iteration. The auxiliary feature factor matrix after the (k+1)th iteration is given. , and It is a constant.

7. A computer device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements the method as described in any one of claims 1-5.

8. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by a processor, it implements the method as described in any one of claims 1-5.

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