Constrained tensor decomposition modeling method for tunnel construction monitoring

Abstract

The embodiment of the invention is suitable for the technical field of tunnel monitoring, and provides a constrained tensor decomposition modeling method for tunnel construction monitoring, and the method comprises the steps: determining a tensor based on tunnel construction monitoring data, the tunnel construction monitoring data comprises a plurality of pieces of sampling data, each piece of sampling data comprises feature data of multiple dimensions, and the feature data of multiple dimensions is obtained; each piece of 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 characteristic factor matrix; optimizing the factor matrix to obtain a target factor matrix meeting time constraint, space constraint and physical constraint; and performing tensor reconstruction according to the target factor matrix to obtain an optimized target tensor. Through the 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 technical field of tunnel monitoring, and particularly relates to a constrained tensor decomposition modeling method for tunnel construction monitoring. Background Art

[0002] During the operation of a tunnel, the health status of the structure is crucial for its safety and reliability. By arranging sensors inside the tunnel, multi-dimensional spatio-temporal 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 failures, data transmission errors, etc., there may be missing data in the collected tunnel monitoring data.

[0004] The incompleteness of the monitoring data will affect the monitoring of the tunnel structure, resulting in inaccurate tunnel construction monitoring. Summary of the Invention

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

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

[0007] Determining a tensor based on tunnel construction monitoring data, where the tunnel construction monitoring data includes multiple sampling data, each sampling data includes feature data in multiple dimensions, and each of the sampling data has corresponding time information and position information;

[0008] Determining the factor matrices of the tensor, where the factor matrices include a time factor matrix, a space factor matrix, and a feature factor matrix;

[0009] Optimizing the factor matrices to obtain target factor matrices that satisfy time constraints, space constraints, and physical constraints;

[0010] According to the target factor matrices, performing tensor reconstruction to obtain an optimized target tensor.

[0011] The second aspect of the embodiments of this application provides a constrained tensor decomposition modeling device for tunnel construction monitoring, including:

[0012] A tensor determination module, configured to determine a tensor based on tunnel construction monitoring data, where the tunnel construction monitoring data includes multiple sampling data, each sampling data includes feature data in multiple dimensions, and each of the sampling data has corresponding time information and position information;

[0013] A matrix determination module, configured to determine factor matrices of the tensor, where the factor matrices include a time factor matrix, a space factor matrix, and a feature factor matrix;

[0014] A matrix optimization module, configured to optimize the factor matrices to obtain target factor matrices that meet time constraints, space constraints, and physical constraints;

[0015] A tensor optimization module, configured to perform tensor reconstruction according to the target factor matrices to obtain an optimized target tensor.

[0016] A third aspect of the embodiments of the present application provides a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, the method described in the first aspect above is implemented.

[0017] A fourth aspect of the embodiments of the present application provides a computer-readable storage medium storing a computer program, and when the computer program is executed by a processor, the method described in the first aspect above is implemented.

[0018] A fifth aspect of the embodiments of the present application provides a computer program product, and when the computer program product runs on a computer device, the computer device is caused to execute the method described in the first aspect above.

[0019] Compared with the prior art, the embodiments of the present application include the following advantages:

[0020] Applying the method in the embodiments of the present application can optimize the tensor corresponding to the tunnel construction monitoring data, making the tensor corresponding to the tunnel construction monitoring data accurate, which is beneficial to tunnel construction monitoring. The computer device can determine the tensor corresponding to the tunnel construction monitoring data. Since the tunnel construction monitoring data includes multiple sampling data, each sampling data includes characteristic data in multiple dimensions, and each sampling data has corresponding time information and position information, therefore, the tensor corresponding to the tunnel construction monitoring data should have corresponding physical characteristics and spatio-temporal characteristics. When performing tensor optimization, the optimized tensor should satisfy physical constraints and spatio-temporal constraints. Therefore, the computer device can decompose the tensor to obtain a time factor matrix, a space factor matrix, and a characteristic factor matrix; then, the computer device can optimize the factor matrices to obtain target factor matrices that satisfy time constraints, space constraints, and physical constraints. Based on the target factor matrices that satisfy time constraints, space constraints, and physical constraints, tensor reconstruction can be performed to obtain an optimized target tensor. The original tensor is determined based on the collected tunnel construction monitoring data, and there may be errors and omissions in the collected tunnel construction monitoring data, so the obtained tensor is not accurate enough. The method in the embodiments of the present application can optimize the tensor corresponding to the tunnel construction monitoring data. The optimized target tensor satisfies time constraints, space constraints, and physical constraints, which is equivalent to correcting the errors and omissions in the original tunnel construction monitoring data in the tensor based on time constraints, space constraints, and physical constraints, thereby obtaining a more accurate target tensor. Conducting tunnel construction monitoring based on the target tensor can improve the accuracy of tunnel construction monitoring. Description of the Drawings

[0021] To more clearly illustrate the technical solutions in the embodiments of the present application, the following briefly introduces the accompanying drawings required for use in the embodiments or the description of the prior art.

[0022] Figure 1 It is a schematic flowchart of the steps of a constrained tensor decomposition modeling method for tunnel construction monitoring provided by an embodiment of the present application;

[0023] Figure 2 It is a schematic flowchart of the steps of another constrained tensor decomposition modeling method for tunnel construction monitoring provided by an embodiment of the present application;

[0024] Figure 3 It is a schematic diagram of a constrained tensor decomposition modeling device for tunnel construction monitoring provided by an embodiment of the present application;

[0025] Figure 4 It is a schematic diagram of a computer device provided by an embodiment of the present application. Detailed Embodiments

[0026] In the following description, specific details such as specific system architectures and technologies are presented for the purpose of illustration rather than limitation, so as to thoroughly understand the embodiments of the present application. However, those skilled in the art should clearly understand that the present application can also be implemented in other embodiments without these specific details. In other cases, detailed descriptions of well-known systems, devices, circuits, and methods are omitted to avoid unnecessary details from interfering with the description of the present application.

[0027] During the operation of a tunnel, the health status of the structure is crucial for its safety and reliability. By arranging sensors inside the tunnel, multi-dimensional spatio-temporal monitoring data such as stress, strain, displacement, and temperature can be obtained. However, this data is large in volume and complex, and traditional analysis methods are difficult to fully extract the potential information therein and cannot effectively predict the future state of the structure.

[0028] Tensor decomposition is an effective tool for processing multi-dimensional data, but traditional tensor decomposition methods fail to consider the physical characteristics of the tunnel structure and the spatio-temporal correlation of the monitoring data, resulting in limited physical interpretability and predictive ability of the model.

[0029] The embodiments of the present application provide a constrained tensor decomposition modeling method for tunnel construction monitoring, thereby being able to improve the accuracy of tunnel construction monitoring.

[0030] The technical solutions of the present application will be described below through specific embodiments.

[0031] Refer to Figure 1 , which shows a schematic flow chart of the steps of a constrained tensor decomposition modeling method for tunnel construction monitoring provided by the embodiments of the present application, and specifically may include the following steps:

[0032] S101, determining a tensor based on tunnel construction monitoring data, where the tunnel construction monitoring data includes a plurality of sampling data, each sampling data includes feature data of a plurality of dimensions, and each of the sampling data has corresponding time information and position information.

[0033] This embodiment can be executed by a computer device. The computer device can be a mobile phone, a tablet computer, a wearable device, a notebook computer, an ultra-mobile personal computer (UMPC), a netbook, a personal digital assistant (PDA), etc. The embodiments of the present application do not impose any restrictions on the specific type of the computer device.

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

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

[0036] S102. Determine the factor matrices of the tensor, where the factor matrices include a time factor matrix, a space factor matrix, and a feature factor matrix.

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

[0038] As an example, the factor matrices of the tensor can be obtained through CP (CANDECOMP / PARAFAC) decomposition. Specifically, using CP decomposition, the tensor is decomposed into the product of three factor matrices. For example, the factor matrices of the tensor are determined by 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] Among them, is the tensor, R is the rank used for tensor decomposition, A is the time factor matrix, B is the space factor matrix, C is the feature factor matrix, represents performing a vector outer product operation.

[0044] S103. Optimize the factor matrices to obtain target factor matrices that meet the time constraint, the space constraint, and the physical constraint.

[0045] ​​​Obtain an auxiliary time factor matrix that satisfies spatiotemporal Kriging constraints, an auxiliary spatial factor matrix that satisfies spatiotemporal Kriging constraints, and an auxiliary feature factor matrix that satisfies physical constraints;

[0046] Based on the auxiliary time factor matrix, the auxiliary spatial factor matrix, and the auxiliary feature factor matrix, construct an optimization formula;

[0047] According to the optimization formula, obtain an optimized target time factor matrix, target spatial factor matrix, and target feature factor matrix.

[0048] Introduce auxiliary factor matrices A0, B0, C0, where A0 is a time factor matrix that satisfies spatiotemporal Kriging constraints, B0 is a spatial factor matrix that satisfies spatiotemporal Kriging constraints, and C0 is a feature factor matrix that satisfies physical constraints.

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

[0050] σ = E·ε

[0051] where σ: stress, E: elastic modulus (known constant), ε: strain.

[0052] Specifically, the representation of the physical constraint in the model. Assume that in the feature dimension, stress and strain correspond to f = 1 and f = 2 respectively. In the feature factor matrix C, take the corresponding rows: C σ = E·C ε .

[0053] Specifically, introduce the spatiotemporal Kriging model as a constraint for the time factor matrix and the spatial factor matrix to describe the correlation in the time and spatial factor matrices. Constraint in the time dimension: Based on the variogram γ T (u) construct the time covariance matrix K T , such that the covariance of the time factor matrix is close to K T : AA T ≈ K T ; Constraint in the spatial dimension: Based on the variogram γ S (h) construct the spatial covariance matrix K S , such that the covariance of the spatial factor matrix is close to K S : BB T ≈ K S .

[0054] Based on the auxiliary time factor matrix, the auxiliary spatial factor matrix, and the auxiliary feature factor matrix, construct an optimization formula, including:

[0055]

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

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

[0058] Convert the optimization formula into multiple iterative formulas, which respectively correspond to the time factor matrix, space factor matrix, and feature factor matrix;

[0059] Based on the iterative formulas, iterate on the time factor matrix, space factor matrix, and feature factor matrix respectively;

[0060] Determine whether the iterated time factor matrix, space factor matrix, and feature factor matrix meet the convergence condition;

[0061] If the convergence condition is met, then take the iterated time factor matrix, space factor matrix, and feature factor matrix as the target time factor matrix, target space factor matrix, and target feature factor matrix respectively;

[0062] If the convergence condition is not met, then execute the target step and the steps after the target step until the convergence condition is met, where the target step is to iterate on the time factor matrix, space factor matrix, and feature factor matrix respectively based on the iterative formulas.

[0063] The iterative formulas include:

[0064]

[0065]

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

[0067] The convergence condition is:

[0068]

[0069] where A k+1 is the time factor matrix after the (k + 1)-th iteration, B k+1 is the spatial factor matrix after the (k + 1)-th iteration, C k+1 is the eigenfactor matrix after the (k + 1)-th iteration, is the auxiliary time factor matrix after the (k + 1)-th iteration, is the auxiliary spatial factor matrix after the (k + 1)-th iteration, is the auxiliary eigenfactor matrix after the (k + 1)-th iteration, and ∈1, ∈2, and ∈3 are constants.

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

[0071] In the embodiments of the present application, the tensor can be optimized, so that the tunnel construction monitoring data can be corrected in the optimized tensor, and based on the optimized tensor, more accurate monitoring results can be obtained.

[0072] The present application proposes a constrained tensor decomposition modeling method, which introduces the physical formula of the tunnel structure and the spatio-temporal Kriging model as constraint conditions into the tensor decomposition process. Through this method, the physical interpretability of the model can be improved, the prediction ability for unobserved data can be enhanced, and a scientific basis can be provided for the safety assessment and maintenance of the tunnel structure.

[0073] Referring to Figure 2 , a schematic flow chart of another constrained tensor decomposition modeling method for tunnel construction monitoring provided by the embodiments of the present application is shown, which may specifically include the following steps:

[0074] S201. Determine a tensor based on tunnel construction monitoring data, where the tunnel construction monitoring data includes multiple sampling data, each sampling data includes characteristic data in multiple dimensions, and each of the sampling data has corresponding time information and location information.

[0075] S202. Determine the factor matrices of the tensor, where the factor matrices include a time factor matrix, a space factor matrix, and a characteristic factor matrix.

[0076] S203. Optimize the factor matrices to obtain target factor matrices that satisfy time constraints, space constraints, and physical constraints.

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

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

[0079] Specifically, the reconstruction error is to calculate the error between the decomposed tensor and the original tensor to evaluate the fitting degree of the model:

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

[0081] Specifically, the spatio-temporal correlation is to calculate and K T The difference between to verify whether the covariance of the time factor matrix meets the expectation.

[0082] Specifically, visualization is to plot the patterns of the factor matrices to observe whether there are obvious structural features. Prediction is to use the decomposition results to predict the structural responses at unobserved positions or future time points and compare them with the actual observed data.

[0083] In this application, first obtain the time factor matrix, space factor matrix, and characteristic factor matrix of the monitoring data group, and based on physical constraints and spatio-temporal Kriging constraints, obtain a constrained tensor of the monitoring data group; compared with the prior art that only uses the time factor matrix, space factor matrix, and characteristic factor matrix to obtain the tensor result of the data, this application uses physical constraints and spatio-temporal Kriging constraints to analyze the data, and the obtained tensor result of the data is more accurate.

[0084] It should be noted that the magnitudes of the sequence numbers of the steps in the above embodiments do not mean 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 to the implementation process of the embodiments of this application.

[0085] Refer to Figure 3, showing a schematic diagram of a constrained tensor decomposition modeling device for tunnel construction monitoring provided by an embodiment of the present application. The device may specifically include a tensor determination module 31, a matrix determination module 32, a matrix optimization module 33, and a tensor optimization module 34, where:

[0086] The tensor determination module 31 is used to determine a tensor based on tunnel construction monitoring data. The tunnel construction monitoring data includes a plurality of sampling data, each sampling data includes feature data in multiple dimensions, and each of the sampling data has corresponding time information and position information;

[0087] The matrix determination module 32 is used to determine the factor matrices of the tensor. The factor matrices include a time factor matrix, a space factor matrix, and a feature factor matrix;

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

[0089] The tensor optimization module 34 is used to perform tensor reconstruction according to the target factor matrices to obtain an optimized target tensor.

[0090] In a possible implementation manner, the factor matrices of the tensor are 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] Where, is the tensor, R is the rank for tensor decomposition, A is the time factor matrix, B is the space factor matrix, C is the feature factor matrix, represents performing a vector outer product operation.

[0096] In a possible implementation manner, the optimizing the factor matrices to obtain target factor matrices that satisfy time constraints, space constraints, and physical constraints includes:

[0097] ​​​Obtain an auxiliary time factor matrix that satisfies spatio-temporal Kriging constraints, an auxiliary spatial factor matrix that satisfies spatio-temporal Kriging constraints, and an auxiliary feature factor matrix that satisfies physical constraints;

[0098] Based on the auxiliary time factor matrix, the auxiliary spatial factor matrix, and the auxiliary feature factor matrix, construct an optimization formula;

[0099] According to the optimization formula, obtain an optimized target time factor matrix, target spatial factor matrix, and target feature factor matrix.

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

[0101]

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

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

[0104] Convert the optimization formula into multiple iterative formulas, which respectively correspond to the time factor matrix, the spatial factor matrix, and the feature factor matrix;

[0105] Based on the iterative formulas, perform iterations on the time factor matrix, the spatial factor matrix, and the feature factor matrix respectively;

[0106] Determine whether the iterated time factor matrix, spatial factor matrix, and feature factor matrix satisfy the convergence condition;

[0107] If the convergence condition is satisfied, then use the iterated time factor matrix, spatial factor matrix, and feature factor matrix as the target time factor matrix, target spatial factor matrix, and target feature factor matrix respectively;

[0108] If the convergence condition is not satisfied, the target step and the steps after the target step are executed until the convergence condition is satisfied, where the target step is to perform iterations on the time factor matrix, the spatial factor matrix, and the feature factor matrix respectively based on the iterative formula.

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

[0110]

[0111] where A k+1 is the time factor matrix after the (k + 1)-th iteration, B k+1 is the spatial factor matrix after the (k + 1)-th iteration, C k+1 is the feature factor matrix after the (k + 1)-th iteration, is the auxiliary time factor matrix after the (k + 1)-th iteration, is the auxiliary spatial factor matrix after the (k + 1)-th iteration, is the auxiliary feature factor matrix after the (k + 1)-th iteration, and are the Lagrange multipliers after the (k + 1)-th iteration, A k is the time factor matrix after the k-th iteration, B k is the spatial factor matrix after the k-th iteration, C k is the feature factor matrix after the k-th iteration, is the auxiliary time factor matrix after the k-th iteration, is the auxiliary spatial factor matrix after the k-th iteration, is the auxiliary feature factor matrix after the k-th iteration, and are the Lagrange multipliers after the k-th iteration, ρ1, ρ2, ρ3 are penalty parameters, is the tensor, E is a constant, and are respectively the rows corresponding to stress and strain in C0.

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

[0113]

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

[0115] In a possible implementation manner, after performing tensor reconstruction based on the target factor matrix to obtain an optimized target tensor, it includes:

[0116] Analyze the tunnel structure according to the target tensor.

[0117] For the device embodiment, since it is basically similar to the method embodiment, the description is relatively simple. For related parts, refer to the description in the method embodiment section.

[0118] Figure 4 is a schematic structural diagram of a computer device provided by an embodiment of the present application. As Figure 4 shown, the computer device 4 of this embodiment includes: at least one processor 40 ( Figure 4 only one is shown in the figure), a memory 41, and a computer program 42 stored in the memory 41 and executable on the at least one processor 40. When the processor 40 executes the computer program 42, it implements the steps in any of the above method embodiments.

[0119] The computer device 4 may be a computing device such as a desktop computer, a notebook, a palm computer, and a cloud computer device. The computer device may include, but is not limited to, a processor 40 and a memory 41. Those skilled in the art can understand that Figure 4 is only an example of the computer device 4 and does not constitute a limitation on the computer device 4. It may include more or fewer components than shown in the figure, or combine some components, or different components. For example, it may also include input / output devices, network access devices, etc.

[0120] The so-called processor 40 may be a Central Processing Unit (CPU), and the processor 40 may also 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. The general-purpose processor may be a microprocessor or the processor may also be any conventional processor, etc.

[0121] In some embodiments, the memory 41 may be an internal storage unit of the computer device 4, such as the hard disk or memory of the computer device 4. In other embodiments, the memory 41 may also be an external storage device of the computer device 4, such as a plug-in hard disk, a Smart Media Card (SMC), a Secure Digital (SD) card, a Flash Card, etc., equipped on the computer device 4. Further, the memory 41 may also include both the internal storage unit and the external storage device of the computer device 4. The memory 41 is used to store an operating system, application programs, a BootLoader, data, and other programs, such as the program code of the computer program. The memory 41 may also be used to temporarily store data that has been output or will be output.

[0122] An embodiment of the present application also provides a computer-readable storage medium storing a computer program, and when the computer program is executed by a processor, the steps in the above-mentioned various method embodiments can be implemented.

[0123] An embodiment of the present application provides a computer program product, and when the computer program product runs on a computer device, the computer device is caused to execute the steps in the above-mentioned various method embodiments.

[0124] The above-mentioned embodiments are only used to illustrate the technical solutions of the present application and are not intended to limit them. Although the present application has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that: they can still modify the technical solutions recorded in the foregoing embodiments, or perform equivalent replacements on some of the technical features; and these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the various embodiments of the present application, and should all be included in the protection scope of the present application.

Claims

1. A constrained tensor decomposition modeling method for tunnel construction monitoring, characterized in that Including: Determine a tensor based on tunnel construction monitoring data, where the tunnel construction monitoring data includes a plurality of sampling data, each sampling data includes characteristic data in multiple dimensions, and each of the sampling data has corresponding time information and position information; Determine the factor matrices of the tensor, where the factor matrices include a time factor matrix, a space factor matrix, and a characteristic factor matrix; Optimize the factor matrices to obtain target factor matrices that satisfy time constraints, space constraints, and physical constraints; According to the target factor matrices, perform tensor reconstruction to obtain an optimized target tensor.

2. The method according to claim 1, wherein Determine the factor matrices of the tensor through the following formula: A = [a1, a2, …, a r , …, a R ​ B = [b1, b2, …, b r , …, b R ​ C = [c1, c2, …, c r , …, c R ​ Among them, is the said tensor, R is the rank for tensor decomposition, A is the said time factor matrix, B is the said spatial factor matrix, and C is the said feature factor matrix. represents performing a vector outer product operation.

3. The method according to claim 1 or 2, characterized in that, The optimizing the factor matrices to obtain target factor matrices that satisfy time constraints, space constraints, and physical constraints includes: Obtain an auxiliary time factor matrix that satisfies spatio-temporal Kriging constraints, an auxiliary space factor matrix that satisfies spatio-temporal Kriging constraints, and an auxiliary characteristic factor matrix that satisfies physical constraints; Based on the auxiliary time factor matrix, the auxiliary space factor matrix, and the auxiliary characteristic factor matrix, construct an optimization formula; According to the optimization formula, obtain an optimized target time factor matrix, target space factor matrix, and target characteristic factor matrix.

4. The method according to claim 3, wherein The constructing an optimization formula based on the auxiliary time factor matrix, the auxiliary space factor matrix, and the auxiliary characteristic factor matrix includes: where ρ1, ρ2, ρ3 are penalty parameters, is the said tensor, A is the said time factor matrix, B is the said spatial factor matrix, C is the said feature factor matrix, A0 is the said auxiliary time factor matrix, B0 is the said auxiliary spatial factor matrix, C0 is the said auxiliary feature factor matrix, E is a constant, and are respectively the rows corresponding to stress and strain in C0.

5. The method according to claim 4, wherein The obtaining an optimized target time factor matrix, target space factor matrix, and target characteristic factor matrix according to the optimization formula includes: Convert the optimization formula into a plurality of iterative formulas, where the iterative formulas correspond to the time factor matrix, the space factor matrix, and the characteristic factor matrix respectively; Based on the iterative formulas, perform iteration on the time factor matrix, the space factor matrix, and the characteristic factor matrix respectively; Determine whether the iterated time factor matrix, space factor matrix, and characteristic factor matrix satisfy the convergence condition; If the convergence condition is satisfied, then use the iterated time factor matrix, space factor matrix, and characteristic factor matrix as the target time factor matrix, target space factor matrix, and target characteristic factor matrix respectively; If the convergence condition is not satisfied, then execute the target step and the steps after the target step until the convergence condition is satisfied, where the target step is to perform iteration on the time factor matrix, the space factor matrix, and the characteristic factor matrix respectively based on the iterative formulas.

6. The method according to claim 5, wherein The iterative formulas include: Among them, A k+1 is the time factor matrix after the (k + 1)-th iteration, B k+1 is the space factor matrix after the (k + 1)-th iteration, C k+1 is the feature factor matrix after the (k + 1)-th iteration, is the auxiliary time factor matrix after the (k + 1)-th iteration, is the auxiliary space factor matrix after the (k + 1)-th iteration, is the auxiliary feature factor matrix after the (k + 1)-th iteration, and are the Lagrange multipliers after the (k + 1)-th iteration, A k is the time factor matrix after the k-th iteration, B k is the space factor matrix after the k-th iteration, C k is the feature factor matrix after the k-th iteration, is the auxiliary time factor matrix after the k-th iteration, is the auxiliary space factor matrix after the k-th iteration, is the auxiliary feature factor matrix after the k-th iteration, and are the Lagrange multipliers after the k-th iteration, ρ1, ρ2, ρ3 are penalty parameters, is the tensor, E is a constant, and are respectively the rows corresponding to the stress and strain in C0.

7. The method according to claim 5, wherein The convergence condition is: Among them, A k+1 is the time factor matrix after the (k + 1)-th iteration, B k+1 is the space factor matrix after the (k + 1)-th iteration, C k+1 is the feature factor matrix after the (k + 1)-th iteration, is the auxiliary time factor matrix after the (k + 1)-th iteration, is the auxiliary space factor matrix after the (k + 1)-th iteration, is the auxiliary feature factor matrix after the (k + 1)-th iteration, and ∈1, ∈2, and ∈3 are constants.

8. The method according to any one of claims 1-2, 4-7, characterized in that, After performing tensor reconstruction according to the target factor matrices to obtain an optimized target tensor, it includes: Analyze the tunnel structure according to the target tensor.

9. 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 according to any one of claims 1-8.

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

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